MathDB

The square of the sum - [IMO LongList 1971]

Source:

January 1, 2011

geometry3D geometryDiophantine equationnumber theory unsolvednumber theory

Problem Statement

Note that

8^3 - 7^3 = 169 = 13^2

and

13 = 2^2 + 3^2.

Prove that if the difference between two consecutive cubes is a square, then it is the square of the sum of two consecutive squares.