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11-XX Number theory
11Bxx Sequences and sets
11B65 Binomial coefficients; factorials; $q$ -identities

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Displaying 41 – 50 of 50

An elementary proof of a congruence by Skula and Granville

Romeo Meštrović (2012)

Archivum Mathematicum

Let $p \geq 5$ be a prime, and let $q_{p} (2) : = (2^{p - 1} - 1) / p$ be the Fermat quotient of $p$ to base $2$ . The following curious congruence was conjectured by L. Skula and proved by A. Granville $q_{p} {(2)}^{2} \equiv - \sum_{k = 1}^{p - 1} \frac{2^{k}}{k^{2}} (mod p) .$ In this note we establish the above congruence by entirely elementary number theory arguments.

An explicit evaluation of the Gosper sum.

Cimadevilla Villacorta, Jorge Luis (2010)

Integers

An extension of the Lucas theorem

Jacques Boulanger, J.-L. Chabert (2001)

Acta Arithmetica

An infinite family of dual sequence identities.

Chapman, Robin (2005)

Integers

An observation on the extension of Abel's lemma.

Patkowski, Alexander E. (2010)

Integers

Another simple proof of the quintuple product identity.

Chan, Hei-Chi (2005)

International Journal of Mathematics and Mathematical Sciences

Asymptotic behavior of Pascal's triangle modulo a prime

Brad Wilson (1998)

Acta Arithmetica

Asymptotic expansion of the equipoise curve of a polynomial inequality.

Eggleton, Roger B., Galvin, William P. (2002)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Asymptotic expansions of certain sums involving powers of binomial coefficients.

Zhao, Chun-Xue, Zhao, Feng-Zhen (2010)

Journal of Integer Sequences [electronic only]

Asymptotic order of the square-free part of $N!$ .

Broughan, Kevin A. (2002)

Integers

Currently displaying 41 – 50 of 50

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