Show that if the difference of the cubes of two consecutive integers is the square of an integer, then this integer is the sum of the squares of two consecutive integers.

(The smallest non-trivial example is: 8^{3} − 7^{3} = 169. This is the square of an integer, namely 13, which can be expressed as 2^{2} + 3^{2}.)

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^{3}− 7^{3}= 169. This is the square of an integer, namely 13, which can be expressed as 2^{2}+ 3^{2}.)## Share this post

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