\section*{Exercise 5 - 031025}

By which numbers is the product of three arbitrary, but consecutive positive integers divisible, whose sum is odd?
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Since the sum is odd, the product consists of two even and one odd factor. Every even number is divisible by 2.

Of three consecutive natural numbers, exactly one is divisible by 3. Of two consecutive even numbers, exactly one is divisible by 4.

Due to the three factors 2, 3, and 4 contained in the product, the product is always divisible by 2, 3, 4, 6, 8, 12, and 24.

Solutions of the II. Round 1963 taken from [5]

\subsection*{7.5.3 III. Round 1963, Class 10}