To the seventh!
In how many ways can six consecutive integers add up to for some integer ?
If you think there are infinitely many ways answer 999999.
The answer is 999999.
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1 solution
6 consecutive integers will add up to 21 + 6m for intgral m. And 21+6m = 3(7+2m), and 7+2m comprises all odd numbers. Therefore, for any odd p we can fin 3^p = 21 + 6m for some m. So, we can make 3^p for all p. That means we can make 3^7, 9^7, 27^7, etc. An infinite number!