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.
(In reply to
without proof of completeness by Charlie)
https://oeis.org/A079584
There is a solution if and only if n>1 and the number of ones in the binary representation of n! is either 1 or 2.
The link has a table that shows there are no solutions (beyond n=2, 3, or 4) below 10,000. The sequence grows quickly, though not monotonically. It's pretty darn clear though that there will not be any solutions beyond 10,000.
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Posted by Jer
on 2023-02-27 14:00:54 |
re: without proof of completeness
