Counting Square-full Solutions to x+y=z
Abstract
We show that there are O(B3/5-3/1555+) triples (x,y,z) of square-full integesr up to B satisfying the equation x+y=z for any fixed >0. This is the first improvement over the `easy' exponent 3/5, given by Browning and Van Valckenborgh. One new tool is a strong uniform bound for the counting function for equations aX3+bY3=cZ3.
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