What will be the remainder when 252^{126} + 2 | vedclass

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(C) To find the remainder when $252^{126} + 244^{152}$ is divided by $10$,we need to find the last digit of the expression.The last digit of $252^{126

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) To find the remainder when $252^{126} + 244^{152}$ is divided by $10$,we need to find the last digit of the expression.The last digit of $252^{126}$ is the same as the last digit of $2^{126}$.The powers of $2$ follow a cycle of $4$: $2^1=2, 2^2=4, 2^3=8, 2^4=16$ (last digit $6$),$2^5=32$ (last digit $2$),and so on.For $2^{126}$,we divide the exponent $126$ by $4$: $126 = 4 	imes 31 + 2$. The remainder is $2$.Thus,the last digit of $2^{126}$ is the same as $2^2 = 4$.Next,the last digit of $244^{152}$ is the same as the last digit of $4^{152}$.The powers of $4$ follow a cycle of $2$: $4^1=4, 4^2=16$ (last digit $6$),$4^3=64$ (last digit $4$),and so on.Since the exponent $152$ is even,the last digit of $4^{152}$ is $6$.Adding the last digits: $4 + 6 = 10$.The last digit of the sum is $0$.Therefore,the remainder when divided by $10$ is $0$.

What will be the remainder when $252^{126} + 244^{152}$ is divided by $10$?

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