- #1
firefly767
- 3
- 0
hi all,
i am wondering how to go about proofs such as the following:
1. if p is an odd prime, show that x^2== a(mod p) has a solution for exactly half the values of a between 1 and p-1 inclusive. if 1<=a<=p-1, and x^2 == a (mod p) has a solution show that it has exactly 2 congrence classes of solutions modulo p.
2. does x^3 == a (mod p) always have a solution for every value of a, when p is prime?
it'll be much appreciated you can also give me some tips as to the ways to approach proofs involving mod, congruence classes (one is exactly the other) etc... thanks in advance!![Smile :smile: :smile:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
i am wondering how to go about proofs such as the following:
1. if p is an odd prime, show that x^2== a(mod p) has a solution for exactly half the values of a between 1 and p-1 inclusive. if 1<=a<=p-1, and x^2 == a (mod p) has a solution show that it has exactly 2 congrence classes of solutions modulo p.
2. does x^3 == a (mod p) always have a solution for every value of a, when p is prime?
it'll be much appreciated you can also give me some tips as to the ways to approach proofs involving mod, congruence classes (one is exactly the other) etc... thanks in advance!