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I was trying do a problem I was stuck , the only remaining to prove was that $2^a+2^b=37k$ where $a(>1),b(>1)$ and $k$ are integers is not possible.

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$2^{18} + 1 = 37\cdot 7085$. Multiply by any power of $2$. – Daniel Fischer Aug 12 '13 at 12:44
edit a and b must be greater than 1 – maths lover Aug 12 '13 at 12:45
@DanielFischer thnx.. – maths lover Aug 12 '13 at 12:46
Ah, well, maybe we can help you solve the problem in some other way? – Daniel Fischer Aug 12 '13 at 12:46

Using $2^{18} + 1 = 37 \cdot 7085$ you can simply take $a = 20$ and $b = 2$ for example and you get $$2^{20}+2^2 = 37\cdot(7085\cdot 4)$$

Any other multiple of two also works as a counter example. The assertion is wrong.

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