Some Diophantine equations and inequalities with primes
Roger Baker
TL;DR
This paper investigates Diophantine equations and inequalities involving sums of prime powers with non-integer exponents greater than one, establishing new ranges of exponents where solutions in primes are abundant.
Contribution
It introduces new ranges of the exponent c for which solutions in primes exist for specific Diophantine inequalities and equations involving sums of prime powers.
Findings
Identified new ranges of c with many solutions in primes
Extended previous results to higher powers and sums
Analyzed equations with integer parts of prime powers
Abstract
The inequalities concern the sum of s powers of primes with non-integer exponent c>1. Here s =2,3,4,or 5. The equations are similar, taking integer part before summing; here s = 3 or 5. New ranges of c are found in all cases for which many solutions in primes exist.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Advanced Mathematical Identities