Two remarks on linear forms in non-negative integers.

on the effect of linear & non-linear texts on students comprehension and recalling

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Representations of Integers by Linear Forms in Nonnegative Integers*

Let Sz be the set of positive integers that are omitted values of the form f = z”= a.x. where the a, are fixed and relatively prime natural numbers *1 $1) and the xi are variable nonnegative integers. Set w = #Q and K = max 0 + 1 (the conductor). Properties of w and K are studied, such as an estimate for w (similar to one found by Brauer) and the inequality 2w > K. The so-called Gorenstein cond...

Linear Forms and Complementing Sets of Integers

Let φ(x1, . . . , xh, y) = u1x1 + · · · + uhxh + vy be a linear form with nonzero integer coefficients u1, . . . , uh, v. Let A = (A1, . . . , Ah) be an h-tuple of finite sets of integers and let B be an infinite set of integers. Define the representation function associated to the form φ and the sets A and B as follows: R (φ) A,B (n) = card ({(a1, . . . , ah, b) ∈ A1 × · · · × Ah × B : φ(a1, ....

A Few Remarks on Linear Forms Involving Catalan’s Constant

Abstract. In the joint work [RZ] of T. Rivoal and the author, a hypergeometric construction was proposed for studing arithmetic properties of the values of Dirichlet’s beta function β(s) at even positive integers. The construction gives some bonuses [RZ], Section 9, for Catalan’s constant G = β(2), such as a second-order Apéry-like recursion and a permutation group in the sense of G. Rhin and C...

Some Remarks on Prime Factors of Integers