Which of the following statements are true ?
A. $2^{202}≡1(modulo\, 5)$
B. $2^{213}≡-2(modulo\, 5)$
C. $2^{300}≡-1(modulo\, 5)$
D. $2^{301}≡2(modulo\, 5)$
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → D only
$2^{301}≡2(\text{modulo 5})$
$(2^4)^{75}.2^2≡2(\text{modulo 5})$
$2=\text{remainder}(\frac{2×1}{5})=2$