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Subjects
11-XX Number theory
11Nxx Multiplicative number theory
11N32 Primes represented by polynomials; other multiplicative structure of polynomial values

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A generalization of a problem of Chebyshev

Jürgen G. Hinz (1996)

Acta Arithmetica

A note on the number of $S$ -Diophantine quadruples

Florian Luca, Volker Ziegler (2014)

Communications in Mathematics

Let $(a_{1}, \dots, a_{m})$ be an $m$ -tuple of positive, pairwise distinct integers. If for all $1 \leq i < j \leq m$ the prime divisors of $a_{i} a_{j} + 1$ come from the same fixed set $S$ , then we call the $m$ -tuple $S$ -Diophantine. In this note we estimate the number of $S$ -Diophantine quadruples in terms of $| S | = r$ .

A quantitative lower bound for the greatest prime factor of (ab+1)(bc+1)(ca+1)

Yann Bugeaud, Florian Luca (2004)

Acta Arithmetica

Almost-primes represented by quadratic polynomials

Robert J. Lemke Oliver (2012)

Acta Arithmetica

Arithmetic properties of polynomial specializations over finite fields

Paul Pollack (2009)

Acta Arithmetica

Currently displaying 1 – 5 of 5

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