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 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.