1,721,020 research outputs found
Two supercongruences related to multiple harmonic sums
No full texthttp://dx.doi.org/10.1017/S000497271200033
Three pairs of congruences concerning sums of central binomial coefficients
No full textRecently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k) = 0 (mod p(2)) for any prime p = 1 (mod 3). In this paper, we provide more examples (with proofs) of congruences of the same kind Sigma([ap/r])(k=1) (2k k)x(k) (mod p(2)) where p is a prime such that p = 1 (mod r), a/r is a fraction in (1/2, 1) and x is a p-adic integer. The key ingredients are the p-adic Gamma function Gamma(p) and a special class of computer-discovered hypergeometric identities
Some congruences for central binomial sums involving Fibonacci and Lucas numbers
No full textWe present several polynomial congruences about sums with central binomial coefficients and harmonic numbers. In the final section we collect some new congruences involving Fibonacci and Lucas numbers
Supercongruences related to 3F2(1) involving harmonic numbers
No full text We provide various supercongruences for truncated series which involve central binomial coefficients and harmonic numbers. The corresponding infinite series are also evaluated. </jats:p
Common fixed points of commuting holomorphic maps of the polydisc which are expanding on the torus
No full text
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