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What 2 digit number is 1 more than a square and 1 less than a cube?

In: Math and Arithmetic [Edit categories]

Answer:

n = x² + 1
n = y³ - 1

x² + 1 = y³ - 1
x^{2 =} y³ - 2
x = (y³ - 2)^.5

This means that you need to find all cubes where subtracting 2 yields a square:
Cubes:
1, 8, 27, 64, 125,...

(-2):
-1, 6, 25, 62, 123,...

(27,25) works.

n = 26

First answer by Pete Miller. Last edit by Pete Miller. Contributor trust: 10 [recommend contributor ]. Question popularity: 2 [recommend question].

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