N*N mod 4.

Number Theory Level 2

Given that $N$ is an even number and is not a multiple of 4, calculate $N\times N \bmod 4$ .

2 solutions

Chew-Seong Cheong
Nov 17, 2018

We can always express an even integer as $N=2n$ , where $n$ is an integer. Then, we have:

$\begin{aligned} N^2 & \equiv 4n^2 \equiv \boxed 0\text{ (mod 4)}\end{aligned}$

All squares of even numbers whether a multiple of 4 or not is divisible by 4.

Srinivasa Gopal
Nov 17, 2018

Let N = (2p) as N is even. So N N = 4 p*p which 4 divides fully without leaving any reminder.