Question

The remainder when $3^{91}$ divided by $80$` is

• A. $3$
• B. $1$
• C. $80$
• D. $27$

Answer 1

The correct option is D $27$

$3\equiv 3mod80$

$3^2=9\equiv 3^{2}mod80$

$9^2=81=1\equiv 3^{4}mod80$

$1^{22}=\equiv (3^4{)}^{22}mod80$

$1\equiv 3^{88}mod80$

$27\equiv 3^{88+3}mod80$

$27\equiv 3^{91}mod80$
Hence the remainder is $27$