The square of a positive integer leaves a remainder of 1 when divided by 5. What are the possible remainders when the integer itself is divided by 5?
n n^2 Remainder when n is divided by 5 1 1 1 4 16 4 6 36 1 9 81 4 11 121 1 14 196 4 16 256 1 19 361 4 21 441 1 24 576 4
There are an infinite number of integers whose squares mod 5 =1 and which leave a remainder of 1 or 4 as you can see on the right hand side.
