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4^61 + 4^62 +4^63 +4^64 +4^65 is divisible by
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4^61
because \(4^{65}=4^{61+4} = 4^{61}\times 4^4\). do the same with the few other numbers and you see clearly that \(4^{61}\) is a common factor.
4^61 + 4^62 +4^63 +4^64 +4^65 =4^61 (1+4+16+64+256) =4^61 *341 = 4^61*11*31 so its divisible by all these 3 4^61,11,31
oh wow...when she first posted it there were no ^'s ..sorry
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