MathDB

4

Part of 1985 Canada National Olympiad

Problems(1)

2^(n-1) | n! if and only if n is a power of 2 [Canada 1985]

Source:

9/30/2011
Prove that 2n−12^{n - 1} divides n!n! if and only if n=2k−1n = 2^{k - 1} for some positive integer kk.
floor functionlogarithmsinequalitiesnumber theoryprime factorization