Reference for a theorem regarding Egyptian fractions

Does anyone have a citation for the following theorem? I’m reasonably confident I’ve seen it before but I don’t have a reference.

Theorem: Let m, n and k be positive integers, . Then the equation 1/x_1 + 1/x_2 + … + 1/x_k = m/n has only finitely many solutions when the x_i are positive integers.

I’ve looked at Ron Graham’s survey of Egyptian Fractions but it doesn’t seem to be there, nor does it seem to be in any other obvious location.

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Nevin Manimala

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