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On the sum of fourth powers in arithmetic progression
Joey M. van Langen
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We prove that the equation (x - y)⁴ + x⁴ + (x + y)⁴ = zⁿ has no integer solutions x, y, z with (x, y) = 1 for all integers n > 1. We mainly use a modular approach with two Frey ℚ-curves defined over the field ℚ( √(30) ).
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