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## Homework Statement

Prove that the expression [tex] \frac{a(a^2 + a)}{3} [/tex] is an integer for all integers [tex] \geq 1 [/tex]

## Homework Equations

## The Attempt at a Solution

[tex] a(a^2 + a ) = 3q + r [/tex]

r can be:

[tex] r = 0,1,2 [/tex]

for r = 0

[tex] \frac{a(a^2 + a)}{3} = q [/tex]

q is an integer by the division algorithm.

When I try this attempt with 3q+1 and 3q+2 I can't get it to work.

Thanks in advance.