(a/p) is legendre symbol not to be confused with 1 divided by p; Prove
Originally Posted by htata123
no one?? this is must be a really tough one.
be patient! also your question is not hard, it's just false! each summand of your sum is either 1 or -1 and we have an odd number of them. so they can never add up to 0.
but then why is it a question on the text book? I'm sure there is a proof because, my professor told us it we had to use the fact (a.b/p) = (a/p).(b/p) and the fact that (a/p) = (a*/p) where a* is the multiplicative inverse of a.
but then why is it a question on the text book? I'm sure there is a proof because, my professor told us it we had to use the fact (a.b/p) = (a/p).(b/p) and the fact that (a/p) = (a*/p) where a* is the multiplicative inverse of a.
i don't know why it's in your text book, but you can see it for yourself that the sum is not 0. for example what do you get for p = 3?
also, are you sure you've posted the question as it is in your text book?