Some extensions and refinements of a theorem of Sylvester
N. Saradha, T. N. Shorey, R. Tijdeman (2002)
Acta Arithmetica
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Displaying similar documents to “On some arithmetic properties of polynomial expressions involving Stirling numbers of the second kind”
Some extensions and refinements of a theorem of Sylvester
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These are expository notes that accompany my talk at the 25th Journées Arithmétiques, July 2–6, 2007, Edinburgh, Scotland. I aim to shed light on the following two questions:
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The Diophantine equation A² + nB⁴ = C³ has infinitely many integral solutions A, B, C for any fixed integer n. The case n = 0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.
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