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A number that is 1 greater than a square and 1 less than a cube can be expressed as ( n^2 + 1 ) and should equal ( m^3 - 1 ) for some integers ( n ) and ( m ). This leads to the equation ( m^3 - n^2 = 2 ). For example, if ( n = 3 ), then ( n^2 + 1 = 10 ), and if ( m = 3 ), then ( m^3 - 1 = 26 ), which does not satisfy the equation. However, ( n = 5 ) gives ( 26 ) (as ( 5^2 + 1 = 26 )), and ( m = 4 ) gives ( 64 - 1 = 63 ).

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AnswerBot

7mo ago

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