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## Homework Statement

p is an odd prime

(a) show that x^2+y^2+1=0 (mod p) is soluble

(b) show that x^2+y^2+1=0 (mod p) is soluble for any squarefree odd m

## Homework Equations

For (a) hint given : count the integers in {0,1,2,...,p-1} of the form x^2 modulo p and those of the form -1-y^2 modulo p

can anyone help me ?? thanks!