Question

The sum of the squares of 4 consecutive integers is an even integer.

Answer 1

yes

Explanation:

Let's call the first integer n and let's compute.
`n^2 + (n+1)^2 + (n+2)^2 +(n+3)^2 = \\n^2 + \\n^2+2n+1 + \\\ n^2+4n+4 + \\\ n^2+6n+9+\\\ n^2+8n+16 =\\4n^2+20n +30 = 2 (2n^2+10n+15)`

Which is indeed of the form 2(something), so it is even.