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congruence of rational numbers

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1: 24.10 Arithmetic Properties
Here and elsewhere two rational numbers are congruent if the modulus divides the numerator of their difference. …
2: Bibliography R
  • H. Rademacher (1973) Topics in Analytic Number Theory. Springer-Verlag, New York.
  • A. Ralston (1965) Rational Chebyshev approximation by Remes’ algorithms. Numer. Math. 7 (4), pp. 322–330.
  • S. Ramanujan (1921) Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.
  • S. Ramanujan (1927) Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,
  • K. H. Rosen (2004) Elementary Number Theory and its Applications. 5th edition, Addison-Wesley, Reading, MA.
  • 3: Bibliography
  • A. Adelberg (1996) Congruences of p -adic integer order Bernoulli numbers. J. Number Theory 59 (2), pp. 374–388.
  • H. Airault (1979) Rational solutions of Painlevé equations. Stud. Appl. Math. 61 (1), pp. 31–53.
  • W. A. Al-Salam and M. E. H. Ismail (1994) A q -beta integral on the unit circle and some biorthogonal rational functions. Proc. Amer. Math. Soc. 121 (2), pp. 553–561.
  • G. E. Andrews and D. Foata (1980) Congruences for the q -secant numbers. European J. Combin. 1 (4), pp. 283–287.
  • H. M. Antia (1993) Rational function approximations for Fermi-Dirac integrals. The Astrophysical Journal Supplement Series 84, pp. 101–108.
  • 4: Bibliography H
  • S. P. Hastings and J. B. McLeod (1980) A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal. 73 (1), pp. 31–51.
  • C. J. Hill (1828) Über die Integration logarithmisch-rationaler Differentiale. J. Reine Angew. Math. 3, pp. 101–159.
  • K. Horata (1989) An explicit formula for Bernoulli numbers. Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.
  • K. Horata (1991) On congruences involving Bernoulli numbers and irregular primes. II. Rep. Fac. Sci. Technol. Meijo Univ. 31, pp. 1–8.
  • I. Huang and S. Huang (1999) Bernoulli numbers and polynomials via residues. J. Number Theory 76 (2), pp. 178–193.