# 3rd January

On this day in 1657, Pierre de Fermat made a challenge to the mathematicians of Europe and England. He posed two problems, involving

1. Find a cube

2. Find a square

Frenicle de Bessy found solutions to these on the day he was given the problems.

*S*(*n*), the sum of the proper divisors of*n*:1. Find a cube

*n*such that*n*+*S*(*n*) is a square.2. Find a square

*n*such that*n*+*S*(*n*) is a cube.Frenicle de Bessy found solutions to these on the day he was given the problems.