Abstract Algebra: Theory and Applications · Problem 7.5.3

Algebraic Coding Theory — Thomas Judson

Mathematics — Abstract Algebra · pseudoprime-base-b

Problem

Let

n

be an odd composite number and

b

be a positive integer such that

\gcd(b, n) = 1

. If

b^{n-1} \equiv 1 \pmod{n}

, then

n

is a pseudoprime base

b

. Show that 341 is a pseudoprime base 2 but not a pseudoprime base 3.