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math.NT2020
Representing an integer as the sum of a prime and the product of two small factors
Roger Baker, Glyn Harman
Let c > 0.55. Every large n can be written in the form p +ab, where p is prime, a and b are significantly smaller than x^1/2 and ab is less than n^c. This strengthens a result of H…
math.NT2020
Some Diophantine equations and inequalities with primes
Roger Baker
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…
math.NT2020
Diophantine approximation with smooth numbers
Roger Baker
We prove a theorem about approximation to an irrational number by rational numbers whose denominator n is free of prime factors bigger than a power of log n. We strengthen the resu…