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Number system book Doubt
by vivek ghiria - Friday, 26 June 2009, 09:37 PM
  Q 13 -
For how many integers S is S/(S-20) square of an integer.

Will it include 0 (zero) also along with 18, 16, and 10.

If 0, do we consider square of 0 = 0

Please guide
Re: Number system book Doubt
by userdce . - Friday, 26 June 2009, 11:19 PM
  see if  
A= S/(S-20)
 is square of any integer then it(A) has to be positive
but value 18,16,10 would make A negative so not possible

it would have two cases for A to be positive
i) S>0 and  S-20>0 ie S>20
ii)S<0 and S-20<0 ie S<0


------------------
I am just trying to solve the problem
assume x2= S/S-20
ie S= 20 [ 1+1/(x2-1)]
now put value of x and see if it gives any integer S


it seems no integer S satisfies this criterion
Re: Number system book Doubt
by vivek ghiria - Saturday, 27 June 2009, 12:23 AM
  I apologies for the typo mistake. Correct question is :

For how many integers S is S/(20-S) square of an integer.
Re: Number system book Doubt
by userdce . - Saturday, 27 June 2009, 12:40 AM
  method is same
ans= 0, -1,+1,-2,+2,-3,+3,

correct me if wrong
Re: Number system book Doubt
by aditya ranjan - Saturday, 27 June 2009, 04:19 AM
  hi every one
this is a simple ques if we go...
s/(20-s) is integer square
so for s<0 denominator gets positive and numerator becomes negative so not possible for any s < 0 ...
now for s=0 ...............we get 1 solution
now for s>0  for s<10 nume<denomi so not possible now start checking from 10 onwards till 20 as after 20 it again becomes negative

so..
0,10,16,18 are the answers
Re: Number system book Doubt
by vivek ghiria - Saturday, 27 June 2009, 10:12 AM
  Hi Aditya

My concern remains : How S=0 will give one solution.
For S=0, expression will be 0/20 = 0 (So is square of 0 is considered as 0 or square of 0 is undefined?)
Re: Number system book Doubt
by Tarun agarwal - Saturday, 27 June 2009, 11:06 AM
 

yes vivek even I faced the same doubt solving this problem.sad

would request TG sir to please illuminate us with correct interpretation.

rgards tarun.

Re: Number system book Doubt
by Navdeep Tuli - Saturday, 18 October 2014, 02:27 PM
  Hi Tarun,
Yes, the square of zero is zero and it is not undefined, it does exist.
Re: Number system book Doubt
by Damini Sarin - Saturday, 30 April 2016, 01:57 PM
  Are we to include zero as the answer?