Vol. 78, No. 1, 1978

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Partitioning integers using a finitely generated semigroup

Daniel Reich

Vol. 78 (1978), No. 1, 233–240
Abstract

Denoting by Γ the semigroup of positive integers generated by two fixed primes, let rk(N) be the number of partitions of N as a sum of k elements of Γ. Our main result is that r2(N) is a bounded function of N. Incidentally, we obtain an estimate of the number of distinct prime divisors of numbers of the form 1 + qn. Boundedness of rk(N) would resolve an approximation theoretic conjecture of D. J. Newman.

Mathematical Subject Classification 2000
Primary: 10A05, 10A05
Secondary: 30E10, 10A45
Milestones
Received: 4 November 1977
Published: 1 September 1978
Authors
Daniel Reich