4

Part of 1976 Spain Mathematical Olympiad

Problems(1)

24 divides (n^5 -5n^3 + 4n)/(n + 2)

Source: Spanish Mathematical Olympiad 1976 P4

Show that the expression

\frac{n^5 -5n^3 + 4n}{n + 2}

where n is any integer, it is always divisible by

24

number theorydivides