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3 results

  • Quadratic Non-Residues and Prime-Producing Polynomials

  • R. A. Mollin, H. C. Williams
  • Journal:
    Canadian Mathematical Bulletin / Volume 32 / Issue 4 / 01 December 1989
    Published online by Cambridge University Press:
    20 November 2018, pp. 474-478
    Print publication:
    01 December 1989
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  • We will be looking at quadratic polynomials having positive discriminant and having a long string of primes as initial values. We find conditions tantamount to this phenomenon involving another long string of primes for which the discriminant of the polynomial is a quadratic non-residue. Using the generalized Riemann hypothesis (GRH) we are able to determine all discriminants satisfying this connection.

  • The Equation Xk + Yk = Zk In Commuting Rational Matrices

  • David E. Rush
  • Journal:
    Canadian Mathematical Bulletin / Volume 26 / Issue 4 / 01 December 1983
    Published online by Cambridge University Press:
    20 November 2018, pp. 406-409
    Print publication:
    01 December 1983
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  • Solutions of Xk + Yk = Zk in invertible pairwise commuting rational 2 × 2 matrices are determined for k = 3, 4, 6, 9, from the analogous results of A. Aigner for algebraic number fields.

  • On the Divisibility of the Class Numbers of Q(√−p) and Q(√−2p) by 16.

  • Philip A. Leonard, Kenneth S. Williams
  • Journal:
    Canadian Mathematical Bulletin / Volume 25 / Issue 2 / 01 June 1982
    Published online by Cambridge University Press:
    20 November 2018, pp. 200-206
    Print publication:
    01 June 1982
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  • Let h(m) denote the class number of the quadratic field Q(√m). In this paper necessary and sufficient conditions for h (m) to be divisible by 16 are determined when m = −p, where p is a prime congruent to 1 modulo 8, and when m = −2p, where p is a prime congruent to ±1 modulo 8.