I need to find all positive integer solutions $(a,b,c)$ to $1+4^a+4^b=c^2$. I am certain that the only solutions are $(t,2t-1, 2^{2t-1}+1) $ and $ (2t-1, t, 2^{2t-1}+1) $ , $t\in \mathbb{N}$ but I am having some trouble confirming this. Could someone help me please? Thank you.
Exponential Diophantine perfect square problem
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number-theory
diophantine-equations
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0Sorry, I should have been more clear. I need help in providing a mathematical proof that those are indeed the only solutions. – 2011-08-12