Small Pythagorean triples modulo prime powers

Abstract

Let $p>5$ be a fixed prime. We obtain an asymptotic formula related to small solutions of quadratic congruences of the form $x_1^2+x_2^2\equiv x_3^2\mathrm{mod}{p}^n$ where $\max \{|x_1|,|x_2|,|x_3|\}\le p^{\hat{I}½n}$ with $\hat{I}½>1/2$.

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