Question

The remainder when $(2222{)}^{5555}$ is divided by 7

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is D

5

(6) 2222 $\equiv$ 3 mod 7 [ a $\equiv$ b mod n means a - b is divisivel by n ]

$(2222{)}^3\equiv$ 27 mod 7 $\equiv$ -1 mod 7

( but 27 $\equiv$ -1 mod 7 )

$\Rightarrow$ $(2222{)}^{5553}\equiv (-1{)}^{1851}$ mod 7 $\equiv$ -1 mod 7

$(2222{)}^2\equiv$ 9 mod 7

$(2222{)}^{5555}\equiv$ -9 mod 7 $\equiv$ 5 mod 7

(but -9 $\equiv$ 5 mod 7 )