MathDB
Z(a,b) is an integer for a \leq b (Austria 2004 -Part1)

Source:

June 18, 2011
factorial

Problem Statement

For natural numbers a,ba, b, define Z(a,b)=(3a)!⋅(4b)!a!4⋅b!3Z(a,b)=\frac{(3a)!\cdot (4b)!}{a!^4 \cdot b!^3}.
(a) Prove that Z(a,b)Z(a, b) is an integer for a≤ba \leq b.
(b) Prove that for each natural number bb there are infinitely many natural numbers a such that Z(a,b)Z(a, b) is not an integer.
Back to ProblemsView on AoPS