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Math Help - Quadratic Residues

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    Quadratic Residues

    We know that there are always 2 consecutive quadratic residues of p if p >= 7 (and p is a prime).

    1.) Show this is true for two diff. primes >= 7

    2.) Prove why this true. (Hint: you will first want to show that at least one of 2, 5, and 10 is a quad. residue of p).
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    Quote Originally Posted by math19091 View Post
    We know that there are always 2 consecutive quadratic residues of p if p >= 7 (and p is a prime).

    1.) Show this is true for two diff. primes >= 7

    2.) Prove why this true. (Hint: you will first want to show that at least one of 2, 5, and 10 is a quad. residue of p).
    An integeristing problem .

    Theorem: Let p be an odd prime the number of quadradic residues (modulo classes) is the same as the number of quadradic non-residues.

    Proof: I can write the prove, but I am sure you learned this theorem.

    Consider our incongruents integers:
    1,2,...,p-1

    The idea is that since the number of quadradic residues is equal to non-residues they MUST be next to each other unless they alternate:

    residue, non-residue, ...
    (Sine 1 is residue).

    But that cannot happen.

    See if you can finish it.
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