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Between the square and the cube

Between the square and the cube

Find a positive integer X less than 1000 such that the number that precedes it (X - 1) be a square, that is to say that it can be expressed as (X - 1) = Y2 and the next number (X + 1) be a cube, that is, it can be expressed as (X + 1) = Z3.

Solution

The only number that meets this property is The 26. You can see the demo on the gaussianos.com page