When (67^{67} + 67) is divided by 68,the rema | vedclass

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(C) To find the remainder when $(67^{67} + 67)$ is divided by $68$,we can use the property of remainders.We know that $(a - 1)^n$ divided by $a$ leave

Vedclass · Accepted Answer

$66$

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(C) To find the remainder when $(67^{67} + 67)$ is divided by $68$,we can use the property of remainders.We know that $(a - 1)^n$ divided by $a$ leaves a remainder of $(-1)^n$ when $a$ is the divisor.Here,$a = 68$ and $n = 67$.So,$67^{67} = (68 - 1)^{67}$.When $(68 - 1)^{67}$ is divided by $68$,the remainder is $(-1)^{67} = -1$.Now,we add the remaining term $67$ to this remainder:Remainder $= -1 + 67 = 66$.Since the remainder must be positive and less than the divisor,the final remainder is $66$.

When $(67^{67} + 67)$ is divided by $68$,the remainder is

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