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1.
We solve the extremal problem of finding the maximum of the functional
?k = 1n ?p = 1mk r( Bk,p,ak,p ), \prod\limits_{k = 1}^n {\prod\limits_{p = 1}^{{m_k}} {r\left( {{B_{k,p}},{a_{k,p}}} \right)}, } 相似文献
2.
B. Uhrin 《Analysis Mathematica》1975,1(2):165-170
В работе для неотрица тельных последовате льностей (...,a ?1 i ), aa 0 i ),a 1 i ), ...), удовлетв оряющих условию \(0< \mathop {\sup }\limits_k a_k^{(i)}< \infty\) (i=1,...,т), доказ а но неравенство
3.
This paper proves three conjectures on congruences involving central binomial coefficients or Lucas sequences.Let p be an odd prime and let a be a positive integer.It is shown that if p=1(mod 4)or a1then where(—)denotes the Jacobi symbol.This confirms a conjecture of the second author.A conjecture of Tauraso is also confirmed by showing that where the Lucas numbers Lo,L_1,L_2,...are defined by L_0=2,L_1=1 and L_n+1=L_n+L_n-l(n=1,2,3,...).The third theorem states that if p=5 then F_p~a-(p~a/5)mod p~3 can be determined in the following way:which appeared as a conjecture in a paper of Sun and Tauraso in 2010. 相似文献
4.
Let p be a prime, χ denote the Dirichlet character modulo p, f (x) = a
0 + a
1
x + ... + a
k
x
k
is a k-degree polynomial with integral coefficients such that (p, a
0, a
1, ..., a
k
) = 1, for any integer m, we study the asymptotic property of
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