EUDML | Note on a Shannon's theorem concerning the Fibonacci numbers and Diophantine quadruples

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Displaying similar documents to “Note on a Shannon's theorem concerning the Fibonacci numbers and Diophantine quadruples”

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We consider the diophantine equation (*) x^p - x = y^q - y in integers (x, p, y, q). We prove that for given p and q with 2 ≤ p < q, (*) has only finitely many solutions. Assuming the abc-conjecture we can prove that p and q are bounded. In the special case p = 2 and y a prime power we are able to solve (*) completely.

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