Some Mathematical Curios  
Presented below are some of the findings that many
CAT 2007 aspirants will find useful and many CAT 2008 aspirants will do well to add them
in their armory early on. Unfortunately, I have not been able to provide the proofs for
these results as the space, as well as the attention span of my readers, is at
a premium. Perhaps, I will do so in my later chapters. Working as a teacher, I
regularly come across useful results that can prove to be beneficial to one's
mathematical health but which do not reach the students because they are not
properly documented. Well, hereon, I promise to document every useful
result/proof that crosses the eyes and grey cells of this Gadha. Feel free to
ask any question that arises in your curious mind. I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.

Re: Some Mathematical Curios  
Hi TG, its great ..really you are doing good job .thanks a ton for this .........

Re: Some Mathematical Curios  
Thx a ton...boss 
Re: Some Mathematical Curios  
Thanks a lot for this awesome rare info...time savers 
Re: Some Mathematical Curios  
Hi, Thanks a ton...really helpful !!! Charu 
Re: Some Mathematical Curios  
TG's magnum opus on display ! 
Re: Some Mathematical Curios  
sir , how do i find the coefficient of x^100 in (1+ x^2 + x^4..) (1 + x^3 + x^ 6.....) (1 + x^5 + x^10...)..... 
Re: Some Mathematical Curios  
thanks boss you r awesome. really u r doing great job. 
Re: Some Mathematical Curios  
Same problem as that of tanmay... 
Re: Some Mathematical Curios  
Hi Kunal and Tanmay, Think! Total Gadha 
Re: Some Mathematical Curios  
it is just terrific!!!!!! no words ,absolutely remarkable article keep it up!!!! 
Re: Some Mathematical Curios  
They r awesome TG.... thnx 4 those blasting tips... 
Re: Some Mathematical Curios  
Hi TG .. It was really very helpful Thanks a lot !! 
Re: Some Mathematical Curios  
17 16 16 14 14 13 12 11 11 9 9 8 7 6 6 4 4 3 2 1 1 
Re: Some Mathematical Curios  
Hey TG, Just two words "HATS OFF ". U amazing. Thanks a 10^10^10^.... in kilos. Ton is not enough. Regards, Srikanth Nair 
Re: Some Mathematical Curios  
Hi TG, Plz tell me how will we get 16 solutions for 2x + 3y = 95? When both c/a and c/b are noninteger we take [ HCF of c/a and c/b ]. Where am I going wrong ? 
Re: Some Mathematical Curios  
Hi TG, Awesome article... Thanks a lot... 8^{95} gives 32 as the last two digits.It has been mentioned wrong in the article.

Re: Some Mathematical Curios  
yep TG 8^{95} gives 32 as the last two digits 
Re: Some Mathematical Curios  
Hi TG, Thanx for solving anand's problem.it cleared mey misconceptions also...but tell me that would we include pairs containing zeros or not???? 
Re: Some Mathematical Curios  
Hai TG, I arrived at finding the no:of odd divisors.Anyway thanks.The materials you provided are awesome!! 
Re: Some Mathematical Curios  
Hi Aditi and Gullz, Corrected. Thanks for pointing that out. Total Gadha 
Re: Some Mathematical Curios  
thanks alot TG... 
Re: Some Mathematical Curios  
Thanks a lot TG! for this nice article. Could you please give answers for the questions given in this article,If possible solutions also. Thanks again! 
Re: Some Mathematical Curios  
This is amazing stuff. Thanks TG. You are simplyyyyyyyyyyyy great.... 
Re: Some Mathematical Curios  
TG in last problem... can u throw light on .... expansion of (xa)^n. thnx 
Re: Some Mathematical Curios  
Good going TG. Thanks for all the effort you're putting in...it shows!! 
Re: Some Mathematical Curios  
great stuff guys. keep going. i am sure this will be of gr8 help for all CAT aspirants. 
Re: Some Mathematical Curios  
Hi TG, I am still waiting for the reply.... Thanks in advance 
Re: Some Mathematical Curios  
Hi TG, how did you find the coefficient of x^100?? in 2x+3y+5z=100 problem 
Re: Some Mathematical Curios  
Hi Vimalesh, Check this out: http://totalgadha.com/mod/forum/discuss.php?d=914#8563 Total Gadha 
Re: Some Mathematical Curios  
Hi TG, Thanks a lot 
Re: Some Mathematical Curios  
Hi TG, I have posted one question on the above link...Please guide me.. Thanks 
Re: Some Mathematical Curios  
Hi TG, I have posted one question on the above link...Please guide me.. Thanks 
Re: Some Mathematical Curios  
Hi Nitesh, It should not be 7^{275} but 7^{273}. Have corrected the typo. Total Gadha 
Re: Some Mathematical Curios  
Hi TG, How come 15 has 4 odd divisors? I am confused please help. 
Re: Some Mathematical Curios  
1,3,5,15 
Re: Some Mathematical Curios  
its ossum . nice article . i found lots of knowledge frm it 
Re: Some Mathematical Curios  
i think m/n=3/5 
Re: Some Mathematical Curios  
Hi TG...U r amazing...Doin a great job.. Am not able to understand hows the last two digits of 8^95 is 32..help me plz.... 
Re: Some Mathematical Curios  
hello, can u plz explain sir 4444 or 6666 or 7777 (written p1 times where p=5) but it is not divisible by 5????? 
Re: Some Mathematical Curios  
Hi Vaibhav, Please read the theorem again. Total Gadha 
Re: Some Mathematical Curios  
Hello TG sir, Please explain this concept with one more example.

Re: Some Mathematical Curios  
Thanxx a lot sir...missed the bracket part initailly... 
Re: Some Mathematical Curios  
hi....... plz plz solve dis problm ....... find remainder when 888888888......................89times is divided by 470.....? 
Re: Some Mathematical Curios  
Some body can solve this problem in a LUCID way. The ans is 278. But the approach was very very hard to understand..so plz help 
Re: Some Mathematical Curios  
For this article...I just want to say WOW..!!!!! 
Re: Some Mathematical Curios  
this is awesome sir,I was wondering if u could send me some thing more like this,pls sir. vignesh 
Re: Some Mathematical Curios  
you have found out number of odd divisors of 15 as 4,but how did u find out? how do you find number of odd divisors of a number ? 
Re: Some Mathematical Curios  
how do you find the coefficient of x^n in (1+x^2+x^4+.....)(1+y^3+y^6+...)(1+z^4+z^8+...) 
Re: Some Mathematical Curios  
hi evryone, pls explain me the method to find out the coefficient of x^100..thanks.. 
Re: Some Mathematical Curios  
hii i stil dunt get to calculate the coefficient of x^{100} in (1 + x^{2} + x^{4} + x^{6} + ...)(1 + x^{3} + x^{6} + ...)(1 + x^{5} + x^{10} + ...) hw to do dat!! plz help 
Re: Some Mathematical Curios  
Hi TG , can you tell the method through binomial of this problem .I guess in binomial there is a method. Suraj 
Re: Some Mathematical Curios  
Hi TG, can you t6ell me how to find the number of digits in a calculation 625^2 * 32^2 * 7 sooraj 
Re: Some Mathematical Curios  
Hi Suraj 625² × 32² × 7 = 5^{8} × 2^{10} × 7 = 28 × 10^{8} is a ten digit number (i.e. 28 followed by eight zeroes.) Kamal Lohia 
Re: Some Mathematical Curios  
Take some example by giving numerical values to the coefficients. That'll help. Kamal Lohia 
Re: Some Mathematical Curios  
Thanks sir But is there any other method......m not comfortable with Grouping & Distribution..... never able to understand it exactly...... 
Re: Some Mathematical Curios  
Hi, whether 22 is divisable by 3, we get a reminder 1 
Re: Some Mathematical Curios  
How 100 can be written as sum of successive positive integers in 2 ways? 