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A (positive definite and non-classic integral) quadratic form is calledstrongly $s$-regular if it satisfies a strong regularity property on the numberof representations of squares of integers. In this article, we prove that forany integer $k \ge 2$, there are only finitely many isometry classes ofstrongly $s$-regular quadratic forms with rank $k$ if the minimum of thenonzero squares that are represented by them is fixed.

Quadratic forms with a strong regularity property on the representations of squares