Square Numbers

The set of square numbers {1, 4, 9, 16, 25, 36, 49, ... } can be represented geometrically by building squares with increasing rows and columns:

                         
                         
                         
                         

ACTIVITY: prove that the sum of two consecutive
triangular numbers is always a square number (picture).

ACTIVITY: can the sum of two squares also be a square?

ACTIVITY: can the sum of two cubes also be a cube?
Can the sum of two fourth powers also be a fourth power?

The Pythagoreans discovered that the sum of certain pairs of square numbers also gives a square number. These numbers are called Pythagorean triples.

Fermat's last theorem



More such numbers
NOVA online: The Proof of FLT