异圈 commented on I Am a Strange Loop by Douglas R. Hofstadter
Content warning A proof that no one asks for
Claim: if p and q are two odd prime numbers that are sum of two squares of prime, then their difference is a multiple of 4
Proof: Say p=a+b and q= c+d, where a, b, c, d are squares of prime number. 1) all of them are odd. Then a-c and b-d are multiples of 4. 2) one of which is 4, but then p-q is odd, contradiction. 3) two of them, say a and c, are 4, they cancel out; b- d is a multiple of 4. QED