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**Combinatorial math question. Please help!!!**

**Prove that the exponent on a prime p in the prime factorization of**

[tex]

\binom{2n}{n}\right)\left

[/tex]

is the number of powers p^k of p such that [2n/p^k] is odd. Use this to determine which primes divide

[tex]

\binom{18}{9}\right)\left

[/tex]

and which divide

[tex]

\binom{20}{10}\right)\left

[/tex]

[tex]

\binom{2n}{n}\right)\left

[/tex]

is the number of powers p^k of p such that [2n/p^k] is odd. Use this to determine which primes divide

[tex]

\binom{18}{9}\right)\left

[/tex]

and which divide

[tex]

\binom{20}{10}\right)\left

[/tex]

**My problem is, I don't even understand this concept in the first place. Can someone please help me to solve this problem as well as recommend me a good book that could help me clarify topics on combinatorial math?**

**Thanks in advance!**