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PL-OM 2002 Problem 1

    Find all the natural numbers a,b,ca,b,c such that:

    1. a2+1a^2+1 and b2+1b^2+1 are primes
    2. (a2+1)(b2+1)=(c2+1)(a^2+1)(b^2+1)=(c^2+1)

    Dataset text AI-MO AoPS. Quoted with source.

    Official text: Polish Mathematical Olympiad 2002 official paper, page 1.

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