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Part BCSIR NET June 2025check-which-form-of-fermat-needs-coprimality-and-which-does-not

Check which form of fermat needs coprimality and which does not

Which of the following statements is true?

  1. A.p ∤ 1 + (p − 1)! for some odd prime p.
  2. B.p | (1234)p−1(1234)^{p-1} − 1 for all primes p > 700.✓ Correct
  3. C.There exist a∈Za \in \mathbb{Z} and a prime p > 11 such that p ∤ aᵖ − a.
  4. D.p ∤ (p2)!/(p!)2(p^{2})!/(p!)^{2} for some odd prime p.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests hypothesis dropped.

See pricing

50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

Related counterexample: If d divides |G| then G has a subgroup of order d

More on this topic

The chapter behind this: Lagrange, orders and cyclic groups — free to read

From Groups › Subgroups, cosets, Lagrange, cyclic groups

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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