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

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Topics in Analytic Number Theory. Springer-Verlag, New York.

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Notes:

Edited by E. Grosswald, J. Lehner and M. Newman, Die Grundlehren der mathematischen Wissenschaften, Band 169

External Links:

MathReview (H. Halberstam), ZentralBlatt

Referenced by:

§1.8(iv), §20.7(viii), §20.7(viii), Ch.24.

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Rational Chebyshev approximation by Remes’ algorithms. Numer. Math. 7 (4), pp. 322–330.

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External Links:

ISSN 0029-599X, Document, MathReview (C. W. Clenshaw), ZentralBlatt

Referenced by:

§3.11(i).

Encodings:

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Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.

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External Links:

ISSN 0025-5874, ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.14(v).

Encodings:

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Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,

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Referenced by:

§24.7(i).

Encodings:

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Elementary Number Theory and its Applications. 5th edition, Addison-Wesley, Reading, MA.

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External Links:

ISBN 0-201-87073-8, MathReview (Norman J. Richert)

Referenced by:

§27.17.

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3: Bibliography

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Congruences of $p$-adic integer order Bernoulli numbers. J. Number Theory 59 (2), pp. 374–388.

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External Links:

ISSN 0022-314X, Document, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.16(iii).

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Rational solutions of Painlevé equations. Stud. Appl. Math. 61 (1), pp. 31–53.

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External Links:

ISSN 0022-2526, MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§32.10(ii), §32.8(i), §32.8(v).

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A $q$-beta integral on the unit circle and some biorthogonal rational functions. Proc. Amer. Math. Soc. 121 (2), pp. 553–561.

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External Links:

ISSN 0002-9939, FullText, MathReview (S. P. Goyal), ZentralBlatt

Referenced by:

§18.33(v).

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Congruences for the $q$-secant numbers. European J. Combin. 1 (4), pp. 283–287.

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External Links:

ISSN 0195-6698, MathReview (J. E. Cigler), ZentralBlatt

Referenced by:

§24.16(iii).

Encodings:

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Rational function approximations for Fermi-Dirac integrals. The Astrophysical Journal Supplement Series 84, pp. 101–108.

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Notes:

Double-precision Fortran, maximum precision 8D.

External Links:

ISSN 0067-0049, Document, Code

Referenced by:

5th item, 1st item.

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4: Bibliography H

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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.

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External Links:

ISSN 0003-9527, Document, MathReview (Richard Brown), ZentralBlatt

Referenced by:

§32.11(ii).

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Über die Integration logarithmisch-rationaler Differentiale. J. Reine Angew. Math. 3, pp. 101–159.

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External Links:

ZentralBlatt

Referenced by:

§25.12(i).

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An explicit formula for Bernoulli numbers. Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.

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External Links:

ZentralBlatt

Referenced by:

§24.6.

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On congruences involving Bernoulli numbers and irregular primes. II. Rep. Fac. Sci. Technol. Meijo Univ. 31, pp. 1–8.

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External Links:

ZentralBlatt

Referenced by:

§24.15(iii).

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Bernoulli numbers and polynomials via residues. J. Number Theory 76 (2), pp. 178–193.

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External Links:

ISSN 0022-314X, Document, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.14(ii).

Encodings:

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