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- Title
FINDING ALMOST SQUARES VII.
- Authors
Tsz Ho Chan
- Abstract
A positive integer n is called an almost square of type 2 if it can be factored in two different ways as n = a1b1 = a2b2 with a1, a2, b1, b2 ≈ √n. We are interested in how short an interval around x, say [x-xφ, x+xφ], contains such kinds of integers. In this note, we improve upon previous upper bounds on φ using exponential sum techniques including recent breakthroughs on Vinogradov's mean value theorem.
- Subjects
EXPONENTIAL sums; MEAN value theorems; INTEGERS
- Publication
Integers: Electronic Journal of Combinatorial Number Theory, 2022, Vol 22, p1
- ISSN
1553-1732
- Publication type
Article