In two previous papers [AGM02,AGM08] we computed cohomology groups H(Γ0(N);C) for a range of levels N , where Γ0(N) is the congruence subgroup of SL4(Z) consisting of all matrices with bottom row congruent to (0, 0, 0, ∗) mod N . In this note we update this earlier work by carrying it out for prime levels up to N = 211. This requires new methods in sparse matrix reduction, which are the main fo...

Let S = {q1, . . . , qs} be a finite, non-empty set of distinct prime numbers. For a non-zero integer m, write m = q1 1 . . . q rs s M , where r1, . . . , rs are non-negative integers and M is an integer relatively prime to q1 . . . qs. We define the S-part [m]S of m by [m]S := q r1 1 . . . q rs s . Let (un)n≥0 be a linear recurrence sequence of integers. Under certain necessary conditions, we ...

Suppose xm+axn is a permutation polynomial over Fp, where p > 5 is prime and m > n > 0 and a ∈ Fp. We prove that gcd(m−n, p−1) / ∈ {2, 4}. In the special case that either (p− 1)/2 or (p− 1)/4 is prime, this was conjectured in a recent paper by Masuda, Panario and Wang.

In this paper we construct a cover {as(mod ns)}s=1 of Z with odd moduli such that there are distinct primes p1, . . . , pk dividing 2 n1 − 1, . . . , 2k − 1 respectively. Using this cover we show that for any positive integer m relatively prime to 15015 there exists an infinite arithmetic progression of positive odd integers the mth powers of whose terms are never of the form 2±p with a, n ∈ {0...

In this paper we construct a cover {as(mod ns)}ks=1 of Z with odd moduli such that there are distinct primes p1, . . . , pk dividing 2 n1 − 1, . . . , 2k − 1 respectively. Using this cover we show that for any positive integer m relatively prime to 15015 there exists an infinite arithmetic progression of positive odd integers the mth powers of whose terms are never of the form 2 + p with p a pr...

in this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. we characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.

For every prime-power q and every pair of natural numbers m n 0 we construct a q-ary linear code of length q m (q n 0 ? 1)(q n 0 ? q n 0 ?m + 1)=(q?1) and dimension 3n 0 ; whose only nonzero weights are q 2n 0 +m?1 ? q 2n 0 ?1 and q 2n 0 +m?1 ? q 2n 0 ?1 + q n 0 +m?1 : These code parameters and those of the corresponding family of strongly regular graphs are new in odd characteristic.

The undirected power graph of a finite group $G$, $P(G)$, is a graph with the group elements of $G$ as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let $A$ be an adjacency matrix of $P(G)$. An eigenvalue $lambda$ of $A$ is a main eigenvalue if the eigenspace $epsilon(lambda)$ has an eigenvector $X$ such that $X^{t}jjneq 0$, where $jj$ is the all-one...

In this paper we construct a cover {as(mod ns)}s=1 of Z with odd moduli such that there are distinct primes p1, . . . , pk dividing 2 n1 − 1, . . . , 2k − 1 respectively. Using this cover we show that for any positive integer m relatively prime to 15015 there exists an infinite arithmetic progression of positive odd integers the mth powers of whose terms are never of the form 2±p with a, n ∈ {0...