A note on the products ((m+1)(2)+1)((m+2)(2)+1) ... (n(2)+1) and ((m+1)(3)+1)((m+2)(3)+1) ... (n(3)+1)

2016-05-01
Gurel, Erhan
We prove that for any positive integer m there exists a positive real number N-m such that whenever the integer n >= m neither the product P-m(n) = ((m + 1)(2) + 1) ((m + 2)(2) + 1) ... (n(2) + 1) nor the product Q(m)(n) = ((m + 1)(3) + 1)((m + 2)(3) + 1) ... (n(3) + 1) is a square.
MATHEMATICAL COMMUNICATIONS

Suggestions

A note on the minimal polynomial of the product of linear recurring sequences
Cakcak, E (1999-08-06)
Let F be a field of nonzero characteristic, with its algebraic closure, F. For positive integers a, b, let J(a, b) be the set of integers k, such that (x - 1)k is the minimal polynomial of the termwise product of linear recurring sequences sigma and tau in F ($) over bar, with minimal polynomials (x - 1)(a) and (x - 1)(b) respectively. This set plays a crucial role in the determination of the product of linear recurring sequences with arbitrary minimal polynomials. Here, we give an explicit formula to deter...
A note on a theorem of Dwyer and Wilkerson
Öztürk, Semra (Springer Science and Business Media LLC, 2001-01-03)
We prove a version of Theorem 2.3 in [1] for the non-elementary abelian group Z(2) x Z(2n), n greater than or equal to 2. Roughly, we describe the equivariant cohomology of (union of) fixed point sets as the unstable part of the equivariant cohomology of the space localized with respect to suitable elements of the cohomology ring of Z(2) x Z(2n).
A short note on permutation trinomials of prescribed type
Akbal, Yildirim; GÜLMEZ TEMÜR, BURCU; Ongan, Pinar (Informa UK Limited, 2019-11-21)
We show that there are no permutation trinomials of the form hox 1/4 x5 ox5oq1 xq1 1 over Fq2 where q is not a power of 2. Together with a result of Zha, Z., Hu, L., Fan, S., hox permutes Fq2 if q 1/4 2k where k 2 omod 4, this gives a complete classification of those q's such that hox permutes F-q(2).
Value sets of folding polynomials over finite fields
Küçüksakallı, Ömer (2019-01-01)
Let k be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra g. We find the cardinality of the value sets of the folding polynomials P-g(k)(x) is an element of Z[x] of arbitrary rank n >= 1, over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.
A note on divisor class groups of degree zero of algebraic function fields over finite fields
Özbudak, Ferruh (Elsevier BV, 2003-01-01)
We give tight upper bounds on the number of degree one places of an algebraic function field over a finite field in terms of the exponent of a natural subgroup of the divisor class group of degree zero.. (C) 2002 Elsevier Science (USA). All rights reserved.
Citation Formats
E. Gurel, “A note on the products ((m+1)(2)+1)((m+2)(2)+1) ... (n(2)+1) and ((m+1)(3)+1)((m+2)(3)+1) ... (n(3)+1),” MATHEMATICAL COMMUNICATIONS, pp. 109–114, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64053.