For a certain positive integer n, n^2 gives a remainder of 4 when divided by 5, and n^3 gives a remainder of 2 when divided by 5. What remainder does n give when divided by 5?

The smallest positive n = 3

3 mod 5 = 3 - the remainder.

The general solution for n is:

n = 5m + 3, where m =0, 1, 2, 3.....etc.

Answered here, too :

https://web2.0calc.com/questions/help-urgent_19