I am a positive integer. If you cube me and then subtract me from the result, the answer is a multiple of 6. Is this statement true for every positive integer, or only specific ones?
True for every positive integer
By algebraic factoring, n^3 - n = n(n-1)(n+1), which is the product of three consecutive integers. Among any three consecutive integers, at least one is even and one is a multiple of 3, meaning the product is always divisible by 6.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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