Applying Gauss's Lemma to Calculate Legendre Symbol (6/13)

[mathsss2]

Use Gauss Lemma (Number theory) to calculate the Legendre Symbol (\frac{6}{13}).

I know how to use Gauss Lemma. However we use the book: Ireland and Rosen. They define Gauss Lemma as:

(\frac{a}{p})=(-1)^n. They say: Let \pm m_t be the least residue of ta, where m_t is positive. As t ranges between 1 and \frac{(p-1)}{2}, n is the number of minus signs that occur in this way. I don't understand how to use this form of Gauss's Lemma

 

[gabbagabbahey]

What are a and p in this case? What does that make \frac{(p-1)}{2} ? What does that make the least residue of ta in this case?

 

[mathsss2]

Could you be more specific, I really do not know how to use this version of Gauss's Lemma. Could you show me some steps on how to start it this way?

 

[gabbagabbahey]

You want to use the lemma for \left( \frac{6}{13} \right), which means you want an "a" and "p" such that \left( \frac{a}{p} \right) = \left( \frac{6}{13} \right) where "p" is a prime...surely you can think of at least one "a" and one "p" for which this will hold true?