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Question Number 152827 by mathdanisur last updated on 01/Sep/21

Answered by MJS_new last updated on 02/Sep/21

$$p=\frac{xy}{x+y}\iff y=\frac{px}{x-p}\iff x=\frac{py}{y-p}$$$$\Rightarrow x>p\wedge y>p\wedge (x-p)\mid \left(px\right)\wedge (y-p)\mid \left(py\right)$$$$\Rightarrow$$$$\left(1\right)y=x\Rightarrow y=x=2p$$$$\left(2\right)y=p+1\Rightarrow x=p(p+1)$$$$\left(3\right)x=p+1\Rightarrow y=p(p+1)$$

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