Prove that ifcis odd, then .

I know I'm supposed to use the theorem that states , wherepis an odd prime. But I'm not confident that stating thatcis simply an odd prime is enough to satisfy this.

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- Nov 24th 2009, 07:51 AMkyldn6Quadratic Residue
Prove that if

*c*is odd, then .

I know I'm supposed to use the theorem that states , where*p*is an odd prime. But I'm not confident that stating that*c*is simply an odd prime is enough to satisfy this. - Nov 24th 2009, 07:38 PMtonio
- Nov 24th 2009, 08:41 PMBruno J.
What is the symbol? The Jacobi symbol? Because the Legendre symbol is defined only for primes. If it's the Jacobi symbol, then it's true and you can prove it using the definition of the Jacobi symbol and the corresponding property of the Legendre symbol.

- Nov 24th 2009, 08:43 PMBruno J.
- Nov 24th 2009, 10:01 PMkyldn6
Yes it is the Jacobi symbol.

- Nov 24th 2009, 10:39 PMBruno J.
Let . By definition, . Using the corresponding property of the Legendre symbol we have that this is . Now what you want to show is .

Does this help a bit? - Nov 24th 2009, 11:06 PMkyldn6
Yes thank you so much.

- Nov 25th 2009, 09:36 PMkyldn6
If its not too much trouble and if someone feels like it, could someone post the last half of the proof, I'm fairly confident I have it here but I'm not 100% confident.