Question

The remainder obtained when $9^{722}$ is divided by 1001 is

• A. 81
• B. 58
• C. 69
• D. 48

Answer 1

The correct option is A

81

$1001=13\times 11\times 7$
$9^{722}$ can be written as $(13n+3)or(11n+4)or(7n+4)$
81 is the least number which satisfies the condition ${}^{\prime }(13n+3)=(11n+4)=(7n+4){}^{\prime }$.
Hence, 81 is the remainder.