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An exploration of hyperpower equations nx = ny
Published online by Cambridge University Press: 01 August 2016
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My interest in this fascinating area of mathematics was aroused by a recent article [1] in which it was shown that
has an infinity of non-trivial solutions (i.e. u ≠ v) in positive integers, rationals and algebraic irrationals. Replacing u and v by their reciprocals, x and y, permits the equation to be written as
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