I am the only prime number that is immediately followed by a positive perfect cube. Which number am I?
7
The number immediately following 7 is 8, which is 2 cubed. Algebraically, n^3 - 1 factors as (n - 1)(n^2 + n + 1). For this product to be prime, the factor (n - 1) must equal 1, meaning n = 2 and n^3 - 1 = 7.
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: Medium. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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