Wyniki wyszukiwania

1

On sums of distinct representatives

100%

Cao H.-Q., Sun Z.-W.

Acta Arithmetica

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1998-1999

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tom 87

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nr 2

159-169

2

Some congruences involving binomial coefficients

100%

Cao H.-Q., Sun Z.-W.

Colloquium Mathematicum

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2015

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tom 139

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nr 1

127-136

EN

Binomial coefficients and central trinomial coefficients play important roles in combinatorics. Let p > 3 be a prime. We show that $T_{p-1} ≡ (p/3) 3^{p-1} (mod p²)$, where the central trinomial coefficient Tₙ is the constant term in the expansion of $(1 + x + x^{-1})ⁿ$. We also prove three congruences modulo p³ conjectured by Sun, one of which is $∑_{k=0}^{p-1} \binom{p-1}{k}\binom{2k}{k} ((-1)^k - (-3)^{-k}) ≡ (p/3)(3^{p-1} - 1) (mod p³)$. In addition, we get some new combinatorial identities.

3

Congruences for Stirling numbers and Eulerian numbers

100%

Cao H.-Q., Pan H.

Acta Arithmetica

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2008

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tom 132

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nr 4

315-328

4

Modifications of the Eratosthenes sieve

100%

Browkin J., Cao H.-Q.

Colloquium Mathematicum

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2014

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tom 135

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nr 1

127-138

EN

We discuss some cancellation algorithms such that the first non-cancelled number is a prime number p or a number of some specific type. We investigate which numbers in the interval (p,2p) are non-cancelled.

Ograniczanie wyników

2 Acta Arithmetica

2 Colloquium Mathematicum

4 Cao H.-Q.

2 Sun Z.-W.

1 Browkin J.

1 Pan H.

1 2015

1 2014

1 2008

1 1998

On sums of distinct representatives

Some congruences involving binomial coefficients

Congruences for Stirling numbers and Eulerian numbers

Modifications of the Eratosthenes sieve