heeeeeeeelp math

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Find the smallest n such that for some prime p, at least 20 of the numbers 1,2,...,n are quadratic non-residues
modulo p.

  • heeeeeeeelp math -

    I suppose this question isn't live anymore. Anyways next time please don't post brilliant problems (:
    Well, here's a few hints for you to work out and be on the right track:
    Step 1: quadratic reciprocity and CRT
    Step 2: incorporate dirichlet's theorem into this.
    Well, you can then see obviously that {3,5,6,7,10,11,12,13,14,17,19,20,22,23,24,26,27,28,29,31}. Now just try to prove that the desired answer is minimal. This is simple. Show that 2 and 3 MUST be quadratic residues.

  • heeeeeeeelp math -

    Ok to clarify, the show that 2 and 3 must be quadratic residues part is to find the minimal.

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