A geometric approach to equal sums of fifth powers |
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Authors: | Andrew Bremner |
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Institution: | Emmanuel College, Cambridge CB2 3AP, England |
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Abstract: | Most of the known results about the Diophantine equation x5 + y5 + z5 = u5 + v5 + w5 are shown to be particular instances of a simple geometrical construction. By studying a K3 surface contained in the fourfold, we show that there are an infinity of parametric solutions also satisfying x + y + z = u + v + w, x ? y = u ? v; and we show that these may be effectively determined. |
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