Question

The remainder when $23^{23}$ is divided by $53$, is

• A. $17$
• B. $21$
• C. $30$
• D. $43$

Answer 1

Answer: (C)

$23^{23}=23\times 23^{22}=23\times (23^2{)}^{11}$
$=23(529{)}^{11}=23(530-1{)}^{11}$
$=23(53m-1)$, $m\in N$
$=23\times 53m-23=53(23m-1)+30$
$\therefore$ Remainder is $30$.