I need to prove that a be a odd integer that congruence X^2[itex]\equiv[/itex]a mod 2(adsbygoogle = window.adsbygoogle || []).push({});

is always solvable with exactly one incongruent solution modulo 2.

this question is linked with (b) let a be an odd integer. Prove that the congruence X^2[itex]\equiv[/itex]a mod 4 is solvable iff a[itex]\equiv[/itex]1 mod 4. in this case ,prove that X^2[itex]\equiv[/itex]a mod 4solutions has exactly two incongruent

solutions modulo 4.

these two seem to link with each other. And the proposition I learn is X^2[itex]\equiv[/itex]a mod p has either no solution or two solutions, but p there is an odd prime number. HOw to apply to the queations above?

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# A question about quadratic residues

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