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Pseudoprimes Based On The Symmetric Functions |
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Of The Roots Of A Polynomial |
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Abstract |
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Given a monic polynomial f with integer coefficients, a symmetric pseudoprime relative to f is defined as a composite integer N such that every elementary symmetric function of the Nth powers of the roots of f is congruent (mod N) to the same function of the first powers. Basic propositions and computational techniques associated with symmetric pseudoprimes are presented, along with specific examples relative to selected polynomials of degrees 1 to 5. |
Introduction |