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I have a question about Legendre symbol or I think that we will use Legendre symbol I am not sure,because I tried to apply the definition of Legendre symbol, quadratic reciprocity and also the properties of Legendre symbol but I could not succeed... Perhaps that question needs something else than Legenndre symbol.

Here is the question:

"Calculate (3/10) and also calculate (2/15)"

Thanks for your help...

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This is not the Legendre symbol, but the Kronnecker symbol, and we have $$ \left( \frac{3}{10}\right)=\left( \frac{3}{2}\right)\left( \frac{3}{5}\right)=-1\cdot (-1)=1. $$ Do the same with $\left( \frac{2}{15}\right)$.

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  • $\begingroup$ thanks dietrich burde.i did not think jacobi. $\endgroup$
    – juliet
    Nov 14, 2013 at 9:37
  • $\begingroup$ Here $(3/2)=-1$ is the Kronnecker symbol $(a/2)$. The Legendre symbol $(a/p)$ is for primes $p\neq 2$. $\endgroup$ Nov 14, 2013 at 10:11

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