Determine all possible triplets (p, q, n) of nonnegative integers that satisfy this equation:
2p + 2q = n!
Provide valid argument for your answer.
*** Adapted from a problem which appeared at the Harvard/MIT math Olympiad.
When converted to binary, 2^p + 2^q will yield a binary number having only two digits equal to 1 and all other digits equal to 0. If you factored every positive integer, converted the result to binary, and then added the sum of the digits, any sum equal to 2 would satisfy the equation.
Using Excel:
3! = 110
4! = 11000
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Posted by hoodat
on 2023-02-28 16:09:47 |
Another approach
