Check which form of fermat needs coprimality and which does not

1. A.p ∤ 1 + (p − 1)! for some odd prime p.
2. B.p | $(1234{)}^{p-1}$ − 1 for all primes p > 700.✓
3. C.There exist $a\in \mathbb{Z}$ and a prime p > 11 such that p ∤ aᵖ − a.
4. D.p ∤ $(p^2)!/(p!{)}^2$ for some odd prime p.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.