Let k,n be integers such that 0 ≤ k ≤ n and 

the binomial coefficient n!;(n - k)!k!, where 0! = 1 and for n > 0, n! = n(n - l)(n - 2)· • ·2· l. 

(a)

(b) 

(c) 

(d) is an integer.

(e) if p is prime and 1 ≤ k ≤ Pⁿ- 1, then is divisible by p. 

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(2)