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}.)

## Question

## BMAD 65

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

## Share on other sites

## 2 answers to this question

## Recommended Posts

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.