This is interesting question of RMO Mock and asked in PRMOYS 2017.
When we repeat a number, i.e. write it twice in a row, we get another number For e.g. repeating '67' gives us the number '6767' Is there any such repeat number which is a perfect square. How many such perfect squares are there?
My approach is that to find any number lets suppose a , we need to multiply with ( 10^n +1) where n is number of digit in a. eg 67 * (10^2+1) = 6767.This will give us repetition,, lets suppose repeat to be b.
(10^n+1) can never be perfect square hence we will spilt it into (p^2xk) and k will be grouped with a like => b = p^2x(k*a).
after doing this i am unable to think and come up with solution. If anyone can provide me with solution would be appreciated.
