Kummer's Theorem provides a connection between the properties of binomial coefficients and their behavior in relation to prime numbers. It states that the highest power of a prime $p$ dividing the binomial coefficient $\binom{n}{k}$ can be determined by analyzing the base $p$ representations of $n$ and $k$. This theorem is particularly important in combinatorics for understanding how primes influence counting problems and the structure of binomial coefficients.
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