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Can Vieta root jumping solve this divisibility problem?

Find all positive integers \((m, n)\) such that \(n+1|m^2+1\) and \(m+1|n^2+1\).

This is pretty much like the problems that we solve by Vieta root jumping method. Can Vieta root jumping solve this divisibility problem? If not, why?

Note by Kazem Sepehrinia
2 months, 3 weeks ago

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I don't think this is that easy. See this for more discussion and a discussion in French here. Chaebum Sheen · 1 week, 3 days ago

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@Chaebum Sheen Thanks for the links :) Kazem Sepehrinia · 1 week, 3 days ago

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I think Vieta jumping is overkill here. Ameya Daigavane · 2 months, 3 weeks ago

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