In this paper we derive a general combinatorial identity in terms of polynomials with dual sequences of coefficients. Moreover, combinatorial identities involving Bernoulli and Euler polynomials areâ€¦ (More)

OBJECTIVE
To compare the efficacy and safety of naphthoquine, artemisinine and a combination of the two drugs in the treatment of faciparum malaria.
METHODS
Of 230 patients, 100 patients wereâ€¦ (More)

Abstract. Let Ïˆ1, Â· Â· Â· , Ïˆk be periodic maps from Z to a field of characteristic p (where p is zero or a prime). Assume that positive integers n1, Â· Â· Â· , nk not divisible by p are their periodsâ€¦ (More)

Let p be a prime, and let f (x) = 0 be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the p-adic order of the sum kâ‰¡r (mod p Î²) n k (âˆ’1) k f k âˆ’ r pâ€¦ (More)

Let G be a finite additive abelian group with exponent exp(G) = n > 1 and let A be a nonempty subset of {1, . . . , n âˆ’ 1}. In this paper, we investigate the smallest positive integer m, denoted byâ€¦ (More)

We establish two general identities for Bernoulli and Euler polynomials, these identities of a new type have many consequences. The most striking result in this paper is as follows: If n is aâ€¦ (More)

Let d > 4 and c âˆˆ (âˆ’d, d) be relatively prime integers, and let r(d) be the radical of d. We show that for any sufficiently large integer n (in particular n > 24310 suffices for 4 6 d 6 36), theâ€¦ (More)

For n = 1, 2, 3, . . . define S(n) as the smallest integer m > 1 such that those 2k(k âˆ’ 1) mod m for k = 1, . . . , n are pairwise distinct; we show that S(n) is the least prime greater than 2nâˆ’ 2â€¦ (More)

Here I give the full list of my conjectures on series for powers of Ï€ and other important constants scattered in some of my public preprints or my private diaries. The list contains totally 181â€¦ (More)