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Question Number 80053 by mr W last updated on 30/Jan/20

$$Findintegerx,ysuchthat$$$$2^x-y^2=615$$

Commented by john santu last updated on 30/Jan/20

$${\left(\sqrt{2^{\mathrm{x}}}\right)}^2-{\left(\mathrm{y}\right)}^2=615$$$$(\sqrt{2^{\mathrm{x}}}-\mathrm{y})(\sqrt{2^{\mathrm{x}}}+\mathrm{y})=615=123\times 5$$$$\sqrt{2^{\mathrm{x}}}+\mathrm{y}=123\wedge \sqrt{2^{\mathrm{x}}}-\mathrm{y}=5$$$$\sqrt{2^{\mathrm{x}}}=64=2^6\Rightarrow \mathrm{x}=12,\mathrm{y}=59$$

Commented by mr W last updated on 30/Jan/20

$$verynicesolution!thanks!$$

Commented by john santu last updated on 30/Jan/20

$$\mathrm{thank}\mathrm{you}\mathrm{mister}$$

Commented by MJS last updated on 30/Jan/20

$$x=12\wedge y=\pm 59$$

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