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2025-02-21 10:56:14

Colin Beveridge on Nostr: nprofile1q…syajh Hello! I asked nprofile1q…aq8c7 about a problem and he said you ...

Hello! I asked about a problem and he said you were the person most likely to have an insight.

I'm trying to solve \( a^2 + b^2 = c^2 + d^2 = e^2 + f^2 = g^2 + h^2 = M^2 \) in the positive integers with \( ef = ab + cd \) and \( gh = ab - cd \), or (I think more likely) prove it can't be done. I've done the obvious thing of breaking the first four expressions into Gaussian integer factors, but then I'm out of my depth.

I'd be glad of anything you can point me at 🙂
Author Public Key
npub1slwuf8as4s8jq9xguyvxvt66zt8wwcjyrnwvcv4mdgle2vha83kshj20hg