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On a generalization of the Frobenius number.

Brown, Alexander, Dannenberg, Eleanor, Fox, Jennifer, Hanna, Joshua, Keck, Katherine, Moore, Alexander, Robbins, Zachary, Samples, Brandon, Stankewicz, James (2010)

Journal of Integer Sequences [electronic only]

On a linear homogeneous congruence

A. Schinzel, M. Zakarczemny (2006)

Colloquium Mathematicae

The number of solutions of the congruence a x + + a k x k 0 ( m o d n ) in the box 0 x i b i is estimated from below in the best possible way, provided for all i,j either ( a i , n ) | ( a j , n ) or ( a j , n ) | ( a i , n ) or n | [ a i , a j ] .

On a system of equations with primes

Paolo Leonetti, Salvatore Tringali (2014)

Journal de Théorie des Nombres de Bordeaux

Given an integer n 3 , let u 1 , ... , u n be pairwise coprime integers 2 , 𝒟 a family of nonempty proper subsets of { 1 , ... , n } with “enough” elements, and ε a function 𝒟 { ± 1 } . Does there exist at least one prime q such that q divides i I u i - ε ( I ) for some I 𝒟 , but it does not divide u 1 u n ? We answer this question in the positive when the u i are prime powers and ε and 𝒟 are subjected to certain restrictions.We use the result to prove that, if ε 0 { ± 1 } and A is a set of three or more primes that contains all prime divisors of any number of the form p B p - ε 0 for...

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