Mixed sums of squares and triangular numbers
Abstract
By means of q-series, we prove that any natural number is a sum of an even square and two triangular numbers, and that each positive integer is a sum of a triangular number plus x2+y2 for some integers x and y with x y (mod 2) or x=y>0. The paper also contains some other results and open conjectures on mixed sums of squares and triangular numbers.
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