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Determine the number of solutions of equation $3^{x} + 4^{x} = 5^{x}$ $3^x+4^x=5^x$

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Answer 1 · 2018-07-10T12:00:35

Only one, the obvious $x = 2$ $x=2$ .

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By Fermat's Last Theorem no natural $x$ $x$ other than two could be a solution; from the graph it's clear $x = 2$ $x=2$ is the only solution.