Sun · The 24-conjecture

Every nonnegative integer n can be written as x²+y²+z²+w² with nonnegative integers x,y,z,w such that both x and x+24y are perfect squares.

four squaresrepresentationsperfect squares

The problem

Every nonnegative integer n can be written as x²+y²+z²+w² with nonnegative integers x,y,z,w such that both x and x+24y are perfect squares.

Open since2017exact formulation date

Last checked2026.07.27Catalog verification

Offer 01$2,400Zhi-Wei Sun

Personal offer

The official slides offer US$2,400 for the first proof.