If \( a, b, p \in \mathbf{N} \) and \( p \) is prime, then \[ (a+b)...

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If \( a, b, p \in \mathbf{N} \) and \( p \) is prime, then
\[
(a+b)^{p}-a^{p}-b^{p}
\]
is divisible by
(a) \( p \)
(b) \( \frac{1}{2} p(p-1) \)
(c) \( p-1 \)
(d) \( p+1 \)
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