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Question Number 175639 by Linton last updated on 04/Sep/22

$$x^{99}+y^{99}=x^{100}$$$$Intergersolutions?$$

Answered by BaliramKumar last updated on 04/Sep/22

$$x^{99}[1+{\left(\frac{y}{x}\right)}^{99}]=x^{100}$$$$1+{\left(\frac{y}{x}\right)}^{99}=x$$$${\left(\frac{y}{x}\right)}^{99}=x-1$$$$\frac{y}{x}=\sqrt[99]{x-1}$$$$y=x\left(\sqrt[99]{x-1}\right)$$$$(0,0)\mathrm{\&}(1,0)$$

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