Let Z be the set of integers, and for a prime p let Zp denote the set of those rational numbers whose denominator is not divisible by p. Let (p ) be the Legendre symbol. Suppose that p is an odd prime and a ∈ Zp. In [7] the author investigated congruences for ∑[p/4] k=0 (4k 2k ) ak modulo p, where [x] is the greatest integer not exceeding x. For k ∈ {0, 1, . . . , p − 1} it is easily seen that ...

thin films of binary bi 0 -teo and bi 0 -v 0 systems were prepared by the thermal co-evaporation technique in a vacuum at room temperature. the optical absorption edge of these systems are studied in the wavelength of 200-800 nm using a perkin-elmer uv/vis spectrophotometer. it is found that the value of n=3/2 in the davis-mott equation is best fitted for the fundamental absorption edge for the...

We study the zeros (mod p) of the polynomial ßp(X) = ¿Zk(Bk/k)(Xp~l~k 1) for p an odd prime, where Bk denotes the k\\\ Bernoulli number and the summation extends over 1 < k < p — 2. We establish a reciprocity law which relates the congruence ßp(r) = 0 (mod p) to a congruence f (n) = 0 (mod r) for r a prime less than/7 and n e Z. The polynomial/ (x) is the irreducible polynomial over Q of the nu...

Let b be an odd integer such that b ≡ ±1 (mod 8) and let q be a prime with primitive root 2 such that q does not divide b. We show that if (pk) q−2 k=0 is a sequence of odd primes such that pk = 2pk−1 + b for all 1 ≤ k ≤ q − 2, then either (a) q divides p0 + b, (b) p0 = q or (c) p1 = q. For integers a, b with a ≥ 1, a sequence of primes (pk) λ−1 k=0 such that pk = apk−1+b for all 1 ≤ k ≤ λ − 1 ...

let $g$ be a finite group and let $gk(g)$ be the prime graph of $g$. we assume that $ngeqslant 5 $ is an odd number. in this paper, we show that the simple groups $b_n(3)$ and $c_n(3)$ are 2-recognizable by their prime graphs. as consequences of the result, the characterizability of the groups $b_n(3)$ and $c_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are obtai...

Abstract In this work, we investigate the quasi-two-body decays $B_c\to D^*h\to D\pi h$ with $h = (K^0,\pi^0,\eta,\eta^{\prime})$ using perturbative QCD(PQCD)&amp;#xD;approach. The description of final state interactions between $D\pi$ pair is achieved through two-meson distribution amplitudes (DAs),&amp;#xD;which are normalized to time-like form factor. PQCD predictions on branching ratios h$&...

Let us suppose that the equation (1) x* + y + z = 0 is satisfied in integers prime to each other and that p is an odd prime. We shall divide the discussion into two parts. We shall refer to the case where xyz is prime to p as Case I, and to the case where xyz = 0 (mod p) as Case II. The present note will be confined to statements of new results obtained by the writer for both cases, without pro...

Abstract In the context of Riordan arrays, problem determining square root a Bell matrix $$R={\mathcal {R}}(f(t)/t,\ f(t))$$ R = ( f t ) / , defined by f...

The purpose of this paper is to complete the classification of binary self-dual [48, 24, 10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c, f) with p being an odd prime, then p = 3, c = 16, f = 0. By considering only an automorphism of type 3-(16, 0), we prove that there are exactly 264 inequivalent self-...

Abstract We present seeing measurements at OAUNI site gathered on 2016 and 2017 campaigns using V R broadband filters. In order to quantify the we used full-width-at-half-maximum from stellar profiles photometric sequences during observational windows of our supernovae program. A typical median <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflo...