Matpic
mathematics, in pictures
Ladder

Sums of two squares — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. 12 lattice points sit on the circle — and 4 × (3 − 0) = 12divisors of 25: 1, 5, 25 are 1 mod 4, none are 3 mod 4

    Two squares, and a lattice

    Whether a prime is the sum of two squares is decided entirely by its remainder on division by four. A fact about circles is settled by a fact about remainders, and neither statement contains any hint of the other.

    rung 1 · number

All ladders