[VA] SRC #008 - 2021 is here !

[Albert Chan]

(01-04-2021 05:56 PM)Gene Wrote:  Biggest number I can see is a portion of the factorial.

No, we would like as many equal numbers as possible.
Say, we partition number N into n parts.

AM-GM inequality:

\(\Large{x_1\,+\,x_2\,+\,x_3\,+\,\cdots\,+\,x_n \over n} \normalsize
≥ \sqrt[n]{x_1\;x_2\;x_3\;\cdots\;x_n}\)

LHS = N/n = constant
RHS = LHS, i.e. maximized products, when \(x_1 = x_2 = x_3 = \cdots = x_n\)