If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?
There are several algebraic ways to solve this question, but the easiest way is as follows: since we cannot have two correct answers just pick a prime greater than 3, square it and see what would be the remainder upon division of it by 12.
n=5 --> n^2=25 --> remainder upon division 25 by 12 is 1.
for the above question if N^2 is divided by 3 or 6 or 8 or 24 then also remainder is always 1.
my question is whether these are the only numbers which when divide N^2 gives the constant remainder or there are other numbers also
which when divide a prime^2 (greater than 3) gives a constant remainder.
i know i am out of topic but if possible do reply because knowing these stuff might save some time in exams.