Question

The remainder when $7^{103}$ is divided by 25 is:

• A. 0
• B. 18
• C. 9
• D. None

Answer 1

The correct option is B

18

$7^{103}=7.(49{)}^{51}=7(50-1{)}^{51}$

= 7$\{{50}^{51}-{}^{51}{C}_1{50}^{50}+....+{}^{51}{C}_{50}.50\}-7$

= 7$\{{50}^{51}-{}^{51}{C}_1{50}^{50}+....+{}^{51}{C}_{50}.50\}-25+18$

$\therefore$ remainder when $7^{103}$ is divided by 25 is 18 .