Re: Modulo Arithmetic â€“ Remainder Theory  
wow,fabulous, fantastic,mind blowing,excellent ...words are short of my dictionary to praise u thanx alot 
Re: Modulo Arithmetic â€“ Remainder Theory  
hey folks how to do 40!%83 
Re: Modulo Arithmetic â€“ Remainder Theory  
how to solve (i) find the remainder of 55555 .... 93 times divided by 98 (ii) remainder of 2 ^1990 / 1990 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Fundoo Bond!!! Just one word.. "Superb".. 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi TG, really an unbelievable article to say the least .... Continue your good work ... Thanks, Jitendra 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi fundoo, Though we all know you are a fundoo and a bond.....by sharing this article to have shown altruistic character.Hats off to you. Thanks Amit 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Fundoo, Wonderful article and great compilation! Thanks! S P 
Re: Modulo Arithmetic â€“ Remainder Theory  
FB Marvelous Methods ! ! ! Thanks, SE 
Re: Modulo Arithmetic â€“ Remainder Theory  
fabulous is the word.....please post some more fundas related to numbers. 
Re: Modulo Arithmetic â€“ Remainder Theory  
Awesome Compilation.Thanks a lot bond 
Re: Modulo Arithmetic â€“ Remainder Theory  
Kudos Fundoo 
Re: Modulo Arithmetic â€“ Remainder Theory  
Re: Modulo Arithmetic â€“ Remainder Theory  
u guyz are jus fantabulous.............thanx a ton......god bless ur species............. 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Fundoo, Its really superb.Only one thing I can say "Fundoo". Thanks and Regards, Manish 
Re: Modulo Arithmetic â€“ Remainder Theory  
bindassss............ rem of 7^115 divided by 114?? 
Re: Modulo Arithmetic â€“ Remainder Theory  
Wonderful job Bond ..... Please post some thing on Permutation and Probability. 
Re: Modulo Arithmetic â€“ Remainder Theory  
7^115 / 114. Phi(114) = 66 hence 7^66 / 114 = 1 Remaining is 7^49 /114 => ((7^3)^16 * 7) / 114 = 1^16 * 7 / 114 = 7 (Since, 7^3 = 343 => 343/114 = 1) 
Re: Modulo Arithmetic â€“ Remainder Theory  
hey, thnx for this article...i hav been lukin for the totient style of solving method since last few months......it was extremely helpful... thnx rohit 
Re: Modulo Arithmetic â€“ Remainder Theory  
thanks . i'll practice & try all this method. It was great . but i have problems in geometry so what i will do ? 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Fundooooooooo, just want to say Tooooooooooooooooooooooooooo Goooooooooooooooooooooooooooooooooooooooooood 
Re: Modulo Arithmetic â€“ Remainder Theory  
helllooo sir .. thankss for such a excellent concept but sir i cldnt be able to take out the print of ths page !! wat shld i do now ? 
Re: Modulo Arithmetic â€“ Remainder Theory  
@mon Haldi ur solution is correct gud solution can u help me in following question 40! mdo 83 
Re: Modulo Arithmetic â€“ Remainder Theory  
This is really a great stuff...and this site is cool hanks a lot... 
Re: Modulo Arithmetic â€“ Remainder Theory  
really a grt..stuff... was actually looking for this one...in a compiled format... and...AAAAHHH!!! here it is .. thx fundoo.. 
Re: Modulo Arithmetic â€“ Remainder Theory  
why can't 41!%83 be 1 ? 
Re: Modulo Arithmetic â€“ Remainder Theory  
@ mon haldi Wilson's Theorem 
Re: Modulo Arithmetic â€“ Remainder Theory  
i dnt mean to say that 41! mod 83 cant be 1 yes it can be 1 or 1 n thus i predicted ans is either 2 or 81 bt which one is correct i dnt knw 
Re: Modulo Arithmetic â€“ Remainder Theory  
2 2 2 2 2 2 2 2 2 2 gud 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hey TG please look at the blog entries and reply my query that I have posted there... 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi TG bt question remains the same what is the exact ans b/w 2 & 81 
Re: Modulo Arithmetic â€“ Remainder Theory  
nice examples to cover all the concepts thank you very much 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi nitin, 1001 is a prime no. if i m nt mistaking...so its euler no. is 1000.hence rem ll be 3?whts d given ans? 
Re: Modulo Arithmetic â€“ Remainder Theory  
No fundoo bond 1001 is not a prime number.It is devisible by 7,11 and 13. The answer is 947. 
Re: Modulo Arithmetic â€“ Remainder Theory  
@ Deep Agrawal  for 7^115 / 114. Phi(114)=36 and not 66.... .i.e. 114(11/2)*(11/3)*(11/19) = 36 therefore we are left with 7^7/114 and 7^3/114=1
=>7^7=7^6.7 =>qstn becomes 7/114= ans=7 
Re: Modulo Arithmetic â€“ Remainder Theory  
@Varun Thanks for pointing it out. Am sorry for the mistake 
Re: Modulo Arithmetic â€“ Remainder Theory  
U r really a champ.. Thanks for the wonderful article... 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi guys This seems quiet Diff prob ..please help Remainder for ..by Chinese theorem (777)^777/1000 
Re: Modulo Arithmetic â€“ Remainder Theory  
Is the answer for this is 72??? i have used euler theorem here....confirm me the answer. 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi all, how do we solve the followin problem: find the remainder when 123412341234.....(89times)is divided by 19? 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi varun!! pretty rite.. thanks 
Re: Modulo Arithmetic â€“ Remainder Theory  
thanku u fundo , it is very useful for me , iam very much in confusion before this .Any way once again thank u 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi everybody..... plz solve (19^36 + 17^36) %111... 
Re: Modulo Arithmetic â€“ Remainder Theory  
Shouldnt phi(63) in the first example be 36 and not 18 as mentioned? It doesnt make a difference to the final answer though 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi Fundoo Bond (777)^777/1001 oops take the question as abv 1000 replaced by 1001(7*11*13) 
Re: Modulo Arithmetic â€“ Remainder Theory  
1. 777^{777}/1000 > Remainder = 797 (Use Binomial to find the last three digits) 2. 644 
Re: Modulo Arithmetic â€“ Remainder Theory  
Nice one TG 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi haldi can you pls explain the remainder theorem u used... substitution of 10^ 2 by 2 
Re: Modulo Arithmetic â€“ Remainder Theory  
Too good...Some of the problems are solved in Arun Sharma's book and it is always good to see alternative solutions to such kind of problems. Regards, Vipul 
Re: Modulo Arithmetic â€“ Remainder Theory  
Just Amazing JOB.....fundoo.. fantastic...stuff. Thanks, HG 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Fundoo Thanks a lot for the article .. 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi... I want the solution for the prblem given below what is the remainder when 7^7^7 is divided by 13... Thanks in advance 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi guys.. got the procedure 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi vamshi is the answer 6??? please confirm 
Re: Modulo Arithmetic â€“ Remainder Theory  
toooooooooooo good...thank you sir. 
Re: Modulo Arithmetic â€“ Remainder Theory  
K=0 
Re: Modulo Arithmetic â€“ Remainder Theory  
really awesome fabulous and excellent ... Thanxx Fundoo Bond.. u did a gr8 job.. Mind blowing 
Re: Modulo Arithmetic â€“ Remainder Theory  
the minimum value of k will be 1. 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi neo.u can find out the answer by the remainder theorm.the answer will be 64 
Re: Modulo Arithmetic â€“ Remainder Theory  
good ,nice theorems ..its time saving a lot .. please help me 2 solve this : find the 3 digit prime no. thats divides 2000!divided by 1000!^2

Re: Modulo Arithmetic â€“ Remainder Theory  
Hey FB U truly are a bond with hell lot of fundas... Thnx. IPS.

Re: Modulo Arithmetic â€“ Remainder Theory  
sir,plz give idea how to solve arun sharma solution what will be remainder 2^2+22^2+222^2 + 2222^2+................+(222........48times)^2%9 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi guy plz accept challenge cat2008 nov16 what is remainder 2^2+22^2+222^2+2222^2.......................+(222......49 times )^2%9 
Re: Modulo Arithmetic â€“ Remainder Theory  
Great work Boss..U r truly TG(total genius....) Fantastic,Mindblowing!!!!! 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi AD P, Anwer to the (2^1990 % 1990) is impressive, but can you explain step LCM(4,198). Why did you take LCM ? Sanjeev 
Re: Modulo Arithmetic â€“ Remainder Theory  
Thanks a lot!I always wondered how to answer such questions.This article was wonderful.do keep posting such articles. 
Re: Modulo Arithmetic â€“ Remainder Theory  
PLZ tell me some1 how to solve......... 1. (100/62)^1/4 2. (100/62)^1/5 3. (100/62)^1/6 
Re: Modulo Arithmetic â€“ Remainder Theory  
PLZ tell me some1 how to solve......... 1. (100/62)^1/4 2. (100/62)^1/5 3. (100/62)^1/6 
Re: Modulo Arithmetic â€“ Remainder Theory  
Thank you for this beautiful article, What is the remainder incase of 13^40 mod 49 ?
Cheers, Sanjeev 
Re: Modulo Arithmetic â€“ Remainder Theory  
don't have words to explain the beauty of this article..solved some difficult question with in second...thanks for this 
Re: Modulo Arithmetic â€“ Remainder Theory  
The article has made life a bit easier when it comes to remainders. 
Re: Modulo Arithmetic â€“ Remainder Theory  
thank you fandu bond for this compilation and you efforts nimish 
Re: Modulo Arithmetic â€“ Remainder Theory  
debashish thanks for d solution......... 
Re: Modulo Arithmetic â€“ Remainder Theory  
Thnxs, I ve another problem. Q .1 Find the 28383rd term of the series: 12345678910111112...........??????

Re: Modulo Arithmetic â€“ Remainder Theory  
hi tg, QUES.find the last digit of the product of all 2 digit numbers that give a remainder of 2 when divided by 5? 
Re: Modulo Arithmetic â€“ Remainder Theory  
pravesh, Is it 6?  SE 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Pravesh QUES.find the last digit of the product of all 2 digit numbers that give a remainder of 2 when divided by 5? 2^{9}*7^{9} = 2*7 = 4 
Re: Modulo Arithmetic â€“ Remainder Theory  
of the product of all 2 digit numbers.......... I missed '2 digit' part and got 2^10 * 7^10 = 4*9 = 6 
Re: Modulo Arithmetic â€“ Remainder Theory  
hello can anybody help me of 63 is given as 18. It should be 36? 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Pushpender, 63=3^2*7 phi(63) = 63(11/7)(11/3) = 36*6/7*2/3 = 36 
Re: Modulo Arithmetic â€“ Remainder Theory  
Really a very helpful and effective article . An eye opener 
Re: Modulo Arithmetic â€“ Remainder Theory  
for the very first question 5^37 / 63 how f(63)=63*(11/3)*11/7=18 . it is 36 how it is confirmed that 5^18/63 remainder is 1 
Re: Modulo Arithmetic â€“ Remainder Theory  
in euler's theorem can some one please explain the calculation of the fucntion pi( n) 
Re: Modulo Arithmetic â€“ Remainder Theory  
Thanks a million ... I always wanted to know how to solve these kind of problems... ... TG .. u Rock ... .... and fundoo... u rule .. 
Re: Modulo Arithmetic â€“ Remainder Theory  
@ remainder when 72! is divided by 73*36! The answer will be 27*36! 
Re: Modulo Arithmetic â€“ Remainder Theory  
How did you get it? 
Re: Modulo Arithmetic â€“ Remainder Theory  
34! is divided by 73 The answer will be 36...No quick method to get this one...You will have to invest a good 3,4 minutes to reach to the answer.. 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi all, anyone pls help me to solve this problem, if x = 777...777 ( 101 7 are there ) then what is x mod 440 ? thanks.. 
Re: Modulo Arithmetic â€“ Remainder Theory  
Your approach to both the questions is correct...And both the answers are also correct.. 
Re: Modulo Arithmetic â€“ Remainder Theory  
thank you antonio..this is the answer..thanks a lot.. 
Re: Modulo Arithmetic â€“ Remainder Theory  
Just Marvellous most remainder questions had me stumped even before i cd start thinkin on them nw i ve got rt d concepts 
Re: Modulo Arithmetic â€“ Remainder Theory  
beautifull explaination thank yuou so s o much. 
Re: Modulo Arithmetic â€“ Remainder Theory  
@ Gowtham Muthukkumaran Thirunavukkarasu with regard to ur solution dated 13 May,2009.... Could u pls explain the last step of ur answer i.e. Remainder of 5*10^99/(9*98)  5/(9*98) 
Re: Modulo Arithmetic â€“ Remainder Theory  
thanx a lot TG.... awesome stuff !! 
Re: Modulo Arithmetic â€“ Remainder Theory  
just did the exercise.. u ve made finding remainder so easy...thnx TG... 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hey, Ho do we find the remainder of 12^107 / 37 ? thanks! 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi TG .. Wannna know how do we evaluate remainder whn question is like a/b^n .. Can it be solved by chinese remainder theorm ? 
Re: Modulo Arithmetic â€“ Remainder Theory  
excellent info...keep up the good work... 
Re: Modulo Arithmetic â€“ Remainder Theory  
i had a prb 1^39+2^39....................12^39 divided by 39 whts the remainder 
Re: Modulo Arithmetic â€“ Remainder Theory  
Extremely useful with all concepts merged into one article... thank you so much TG! 
Re: Modulo Arithmetic â€“ Remainder Theory  
Can someone have shortcuts method to get remainder of the below expression: (26^5 + 27^5 + 28^5 + 29^5) divided by 110 ? Options are 1) 0 2) 2 3) 55 4) 4 5) 5 
Re: Modulo Arithmetic â€“ Remainder Theory  
Ans is option 1) 0 since a^n + b^n + c^n +... is divisible by a+b+c+.... when n is odd. 
Re: Modulo Arithmetic â€“ Remainder Theory  
Thanks Karthikeyan Santhanam But could you provide me general a way to solve this type of question, suppose if n would be even then what should have ones approach? Thanks once again. 
Re: Modulo Arithmetic â€“ Remainder Theory  
@ROHIT K ya u got the correct answer n I understand ur approach, it was quite helpful . Thnks buddy 
Re: Modulo Arithmetic â€“ Remainder Theory  
tooooooooooooooo goooooooooood thanx!!!11 they helped a lot. 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hey guys...can u tell me the ans to this : Find the remainder when 3^1000/91. Its simple yet the ans is simply eluding me... SOS!!! Sudi 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Sudipto ans I got is 81.please check 
Re: Modulo Arithmetic â€“ Remainder Theory  
hii 7^7/114 and 7^3/114=1
=>7^7=7^6.7 =>qstn becomes 7/114= ans=7 can u xpalin dis step?? 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi ol!! What is the digit at the hundredths place of the number N = 45^{36} ? can u help me findin soln tu dis problem thanx in advance kanika 
Re: Modulo Arithmetic â€“ Remainder Theory  
thanxz a ton arun 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi 723^{243} + 318^{243} is divided by 17? teme hw 2 go abt it? 
Re: Modulo Arithmetic â€“ Remainder Theory  
hey shankaranathan soryy d ans s 9. can sumbdy teme d soln? n ya!! teme d answer of ques u askd!! 21^22 % 125 is d ans 1? 
Re: Modulo Arithmetic â€“ Remainder Theory  
thanz arun!! dat ws gr8!! 
Re: Modulo Arithmetic â€“ Remainder Theory  
Phi(63) is 36 not 18.. 
Re: Modulo Arithmetic â€“ Remainder Theory  
hi can anybody tell me the solution of the following? 5^400 divided by 1309. find the remainder. ans: 1 please tell me if it can be done using euler's theorem. 
Re: Modulo Arithmetic â€“ Remainder Theory  
HI sahil ..see this thread: http://totalgadha.com/mod/forum/discuss.php?d=6268 
Re: Modulo Arithmetic â€“ Remainder Theory  
Find the last two digits of 2^2^2003..plz post the approach 
Re: Modulo Arithmetic â€“ Remainder Theory  
is the answer 2? 
Re: Modulo Arithmetic â€“ Remainder Theory  
Please solve: remainder when 2^133 is divided by 133 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Sukriti 133 = 7*19 So find the remainder of 2^{133} with 7 and 19 individually and then combine them using Chinese Remainder Theorem. 
Re: Modulo Arithmetic â€“ Remainder Theory  
Hey can anyone tell me how to solve this? x2222....16times divide by 17 gives remainder of 0 Find x 
Re: Modulo Arithmetic â€“ Remainder Theory  
Can anyone pls help me to find the remainder of 28! when divided by 67....any shortcut!!!! 
Re: Modulo Arithmetic â€“ Remainder Theory  
Thanks a lot sir 
Re: Modulo Arithmetic â€“ Remainder Theory  
128^100/153.??? plz solve dis 
Re: Modulo Arithmetic â€“ Remainder Theory  
42....is it crrect?/ 
Re: Modulo Arithmetic â€“ Remainder Theory  
With all due respect! the equation ax+by=1 in the chinese remainder theorem should be ax+by=1 else the solution will be incorrect. 
Re: Modulo Arithmetic â€“ Remainder Theory  
too gud.... thanx..... 
Re: Modulo Arithmetic â€“ Remainder Theory  
exlnt page thanx a lot.. it helpd me a lot 
Re: Modulo Arithmetic â€“ Remainder Theory  
@ AD P it is clear but cant be able to get ehy you have taken LCM of the eulars?

Re: Modulo Arithmetic â€“ Remainder Theory  
Hi Neha You can purchase the Ebooks at this page CAT Products, which contain solutions to the problems in quizzes at this site. Otherwise you are always welcome to post your doubts and get them solved here only. 
Re: Modulo Arithmetic â€“ Remainder Theory  
In your solution you said x can be only 2 or 81. How to find these values. 2 can be found by trial and error. But how to find 81? 
Re: Modulo Arithmetic â€“ Remainder Theory  
awesome article..although i couldnt understand..how 3^41/77 became..3^4/77...plz somebody explain this to me.. Thanks 
Re: Modulo Arithmetic â€“ Remainder Theory  
2^11/25 yield 23 as remainder 
Re: Modulo Arithmetic â€“ Remainder Theory  
please find the remainder for (4^79)/81 using euler's theorem... 
Re: Modulo Arithmetic â€“ Remainder Theory  
I have a dbt in examples of Euler's theorem.. 1. hw come 63(11/3)(11/7)=18??shudn't it b 36?? 2. n also 1000(11/2)(11/4)=400?? shudn't be 375?? 
Re: Modulo Arithmetic â€“ Remainder Theory  
Ohkk..Thanks sir. 
Re: Modulo Arithmetic â€“ Remainder Theory  
BUT IN 2^1990 MOD 1990 ,2 AND 1990 ARE NOT COPRIME SO HOW CAN WE APPLY EULER THEOREM 