If m and n are even numbers, which of the following could be the value of m^2 + n^2?

Question

How to approach this question?

Nik D · Accepted Answer

Since m and n are even numbers, we can express them as:m = 2an = 2bwhere a and b are integers.
We need to find the possible values of m^2 + n^2. Substituting m and n in terms of a and b:
m^2 + n^2 = (2a)^2 + (2b)^2 = 4a^2 + 4b^2 = 4(a^2 + b^2)
Since a^2 + b^2 is an integer, we know that 4(a^2 + b^2) must be a multiple of 4.Therefore, the value of m^2 + n^2 must also be a multiple of 4.

­If m and n are even numbers, which of the following could be the value of m^2 + n^2?

If m and n are even numbers, which of the following could be the value of m^2 + n^2?