Prove For all integers n if n2 0mod 3 then n 0mod 3Solutionn

Prove: For all integers n, if n² 0(mod 3), then n 0(mod 3).

n^2=0 mod 3

HEnce , n^2=3k for some intger k

Hence, 3|n^2

Assume, 3 does not divide n

So, 3 is not present in prime factorisation of n

HEnce, 3 is not present in prime factorisation of n^2

But,3|n^2. So a contradiction.

Hence, 3|n