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Abstract Algebra

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Divisibility Properties of Factorials and Factorials Plus One

ABSALG-EGQXGI

Which of the following statements is TRUE?

A calculator is not needed.

Hint: The notation $n!$ means $n$ factorial, defined as the product $1.2.\ldots.(n-1).n$ of all integers from $1$ to $n$. A composite number is an integer that is not prime.

Select ALL that apply.

A

$4$ divides $(4-1)!+1$

B

If an integer $m>1$ is composite, then $m$ divides $(m-1)!+1$

C

$(5-1)!+1$ is divisible by $5$

D

$(5-1)!+1$ is divisible by $25$

E

$6$ does not divide $(6-1)!$