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Quadric hypersurfaces are well‐known to satisfy the Hasse principle. However, this is no longer true in the case of the Hasse principle for integral points, where counter‐examples are known to exist in dimension 1 and 2. This work explores the frequency that such counter‐examples arise in a family of affine quadric surfaces defined over the integers.

Failures of the integral Hasse principle for affine quadric surfaces