2020 CAMO Problems/Problem 2

Problem 2

Let $k$ be a positive integer, $p>3$ a prime, and $n$ an integer with $0\le n\le p^{k-1}$. Prove that \[\binom{p^k}{pn}\equiv\binom{p^{k-1}}n\pmod{p^{2k+1}}.\]


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See also

2020 CAMO (ProblemsResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6
All CAMO Problems and Solutions

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