Finding Almost Squares VII
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.
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