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National and Regional Contests
Belgium Contests
Flanders Math Olympiad
2001 Flanders Math Olympiad
1
divisibility
divisibility
Source:
August 8, 2004
Problem Statement
may be challenge for beginner section, but anyone is able to solve it if you really try. show that for every natural
n
>
1
n > 1
n
>
1
we have:
(
n
−
1
)
2
∣
n
n
−
1
−
1
(n-1)^2|\ n^{n-1}-1
(
n
−
1
)
2
∣
n
n
−
1
−
1
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