26 citations · 35 across the 6 of their papers we have counts for
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Denser Egyptian Fractions
Greg Martin
An Egyptian fraction is a sum of distinct unit fractions (reciprocals of positive integers). We show that every rational number has Egyptian fraction representations where the numb…
Uniform Bounds for the Least Almost-Prime Primitive Root
Greg Martin
We investigate, using the weighted linear sieve, the distribution of almost-primes among the residue classes (mod p) that generate the multiplicative group of reduced residue class…
The Least Prime Primitive Root and the Shifted Sieve
Greg Martin
We derive, for all prime moduli p except those in a very thin set, an upper bound for the least prime primitive root (mod p) of order of magnitude a constant power of log p. The im…
Lower Bounds for the Number of Smooth Values of a Polynomial
Greg Martin
We investigate the problem of showing that the values of a given polynomial are smooth (i.e., have no large prime factors) a positive proportion of the time. Although some results…
Solubility of Systems of Quadratic Forms
Greg Martin
We derive an upper bound for the least number of variables needed to guarantee that a system of t quadratic forms (t>=2) over a field F has a nontrivial zero. In particular, if F i…
Dense Egyptian Fractions
Greg Martin
Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large…