Question

What is the remainder when ${74}^{13}-{41}^{13}+{76}^{13}-{42}^{13}$ is divided by $66?$

• A. $0$
• B. $64$
• C. $1$
• D. none of these

Answer 1

Answer: (A)

$0$

$\frac{{74}^{13}-{41}^{13}+{75}^{13}-{42}^{13}}{66}\Rightarrow$ Remainder

Concept: $\frac{a^n-b^n}{a-b}$ remainder will be zero.

$\frac{{74}^{13}+{41}^{13}}{33\times 2}+\frac{{75}^{13}-{42}^{13}}{33\times 2}$

$\Rightarrow 74-41=33$ & $75-42=33$

From the above concept remainder will be zero.