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    Number Theory Perfect Square

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    Is there a perfect square n^2 such that

    n^2 = -1 (mod p) for

    p=3
    p=5
    p=7
    p=11
    p=13
    p=17
    p=19?

    Can you characterize the primes for which n^2 = -1 (mod p) has a solution?

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    https://brainmass.com/math/number-theory/number-theory-perfect-square-35171

    Solution Preview

    Sol: If a = b (mod k), then b = a + mk, where m is an integer.
    Here, n^2 = -1 (mod p) implies that -1 = n^2 + mp, where m is an ...

    Solution Summary

    The number theory for perfect squares are determined.

    $2.49

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