Homework Statement
Let p be a prime, k be positive integer, and m ∈ {1, 2, 3, ..., pk-1}. Without using Lucas' theorem, prove that p divides \binom{p^k}{m}.
Homework Equations
The definition of the binomial coefficients: \binom{a}{b} = \frac{a!}{b! (a-b)!}
The Attempt at a Solution
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