P2

Part of 2024 Philippine Math Olympiad

Problems(1)

Double factorial divisibility

Source: Philippine Mathematical Olympiad 2024 P2

0!!=1!!=1

n!!=n\cdot (n-2)!!

for all integers

n\geq 2

. Find all positive integers

n

\dfrac{(2^n+1)!!-1}{2^{n+1}}

factorialnumber theory