Legendre symbols with huge "p"s

Question

I am in doubt with an exercise - I need to calculate $$\left(205\mid853\right)$$

I would use the fact Legendre's symbols are multiplicative, but then I would have something like

$$\left(5\mid853\right)\left(41\mid853\right)$$

and it would not help much with Gauss lemma, since it would mean having sequences $(853-1)/2$ longs to multiply, to operate $\mod 853$, and so on.

Is there a faster trick I don't see?

Thanks in advance.

$(205 |853)=-1$. see http://www.wolframalpha.com/input/?i=what+are+the+quadratic+residue+modulo+853. — Dietrich Burde, Apr 25 '14 at 13:07

score 0 · Answer 1 · answered Apr 25 '14 at 09:16

0

If you can't solve the problem with this tool, please comment out and I'll write a more complete answer.

answered Apr 25 '14 at 09:16

ajotatxe

That solves - but I cannot use it, unfortunately is not in the programme of this course. – user128857 Apr 25 '14 at 09:23
Then, as far as I know, the only way is brute force. Can you use a computer program? – ajotatxe Apr 25 '14 at 12:10

1 Answers1