Is the sum of three consecutive integers always divisible by 3?

Question

Hint: What does adding three consecutive integers abstractly look like? Can we divide this sum by 3?

Answer 1

Test it. The 3 consecutive integers are

n

n + 1

n + 2

Their sum is

n + (n + 1) + (n + 2) = 3n + 3 = 3(n + 1)

Note this is divisible by 3.