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2-x-y-2-7-x-y-N-x-y-




Question Number 168672 by mathlove last updated on 15/Apr/22
2^x =y^2 +7         x,y∈N  x=?                  y=?
$$\mathrm{2}^{{x}} ={y}^{\mathrm{2}} +\mathrm{7}\:\:\:\:\:\:\:\:\:{x},{y}\in{N} \\ $$$${x}=?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}=? \\ $$
Commented by safojontoshtemirov last updated on 15/Apr/22
x=3   y=1    x=7    y=11  x=4   y=3  x=5   y=5
$${x}=\mathrm{3}\:\:\:{y}=\mathrm{1}\:\:\:\:{x}=\mathrm{7}\:\:\:\:{y}=\mathrm{11} \\ $$$${x}=\mathrm{4}\:\:\:{y}=\mathrm{3} \\ $$$${x}=\mathrm{5}\:\:\:{y}=\mathrm{5} \\ $$
Commented by Rasheed.Sindhi last updated on 16/Apr/22
Also  x=15,y=181  ...  ..
$${Also} \\ $$$${x}=\mathrm{15},{y}=\mathrm{181} \\ $$$$… \\ $$$$.. \\ $$
Commented by Rasheed.Sindhi last updated on 16/Apr/22
2^x =y^2 +7         x,y∈N  2^x =y^2 +7⇒y^2 +7∈E⇒y^2 ∈O⇒y∈O
$$\mathrm{2}^{{x}} ={y}^{\mathrm{2}} +\mathrm{7}\:\:\:\:\:\:\:\:\:{x},{y}\in{N} \\ $$$$\mathrm{2}^{{x}} ={y}^{\mathrm{2}} +\mathrm{7}\Rightarrow{y}^{\mathrm{2}} +\mathrm{7}\in\mathbb{E}\Rightarrow{y}^{\mathrm{2}} \in\mathbb{O}\Rightarrow{y}\in\mathbb{O} \\ $$

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