gronau'sconjecture

Gronau's Conjecture

Hi!

Exists a proof, that for every prime p > X with p = 8n + 3 :

p = a^2 + b^2 + c^2 ? And what is X?

Thanks a lot!

Daniel Gronau

1) Consider any m=8n+3, not necessarily prime, p

2) Consider a, b, c odd only

3) Consider differences of successive odd squares.

1^2+1^2+1^2 = 3

3^2+1^2+1^2 = 11

3^2+3^2+1^2 = 19

5^2+1^2+1^2 = 27 ... etc.

3^2-1^2 = 8

5^2-3^2 = 16

7^2-5^2 = 24

9^2-7^2 = 32 ... etc.