What are all of the positive integer solution pairs (n, k) for the following equations? From easiest to hardest, IMO...
n! + 7 = 2^k
n! + 10 = 2^k
n! + 8 = 2^k
All these equations are identical except for the constant term, which means they require slightly different strategies. It's easy to inspect solutions for small values of n & k, but the tougher part is proving there is a bound on what n can be.
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