I am a positive integer. When you cube me and then subtract me from the result, the answer is a multiple of 6. What am I? (Give the smallest possible value greater than 1)
2
For any integer n, n^3 - n can be factored as n(n-1)(n+1), which is the product of three consecutive integers. One of these must be a multiple of 2 and one a multiple of 3, meaning the product is always divisible by 6. For n=2, 2^3 - 2 = 8 - 2 = 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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