I am Ok now, i just though a bit far. Thanks for your help! I get the idea now! many thanks!

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- Oct 21st 2013, 03:26 PMSonifaRe: equation soluble
I am Ok now, i just though a bit far. Thanks for your help! I get the idea now! many thanks!

- Oct 21st 2013, 03:32 PMSlipEternalRe: equation soluble
I just don't understand where the confusion comes from. If you find x_i, y_i. s.t. x_i^2+y_i^2+1 = 0 (mod p_i), then use the Chinese Remainder Theorem to find x and y, then x=x_i (mod p_i), y=y_i (mod p_i). So x^2+y^2+1 = x_i^2+y_i^2+1 (mod p_i)

- Oct 21st 2013, 03:54 PMSonifaRe: equation soluble
I considered not for every primes then x y may have not more than one solution, how comes whatever i take can satify the conditon. For me , now , every thing is clear, and thanks for all the help to me :D