Find-integer-x-y-such-that-2-x-y-2-615-

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

F i n d i n t e g e r x, y s u c h t h a t

2^{x} - y^{2} = 615

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

{(\sqrt{2^{x}})}^{2} - {(y)}^{2} = 615

(\sqrt{2^{x}} - y) (\sqrt{2^{x}} + y) = 615 = 123 \times 5

\sqrt{2^{x}} + y = 123 \land \sqrt{2^{x}} - y = 5

\sqrt{2^{x}} = 64 = 2^{6} \Rightarrow x = 12, y = 59

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

v e r y n i c e s o l u t i o n! t h a n k s!

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

thank you mister

Commented by MJS last updated on 30/Jan/20

x = 12 \land y = \pm 59

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