Find the remainder of 241-41

We know that A^p 1÷ p, leaves a remainder of 1, when p is a prime number. Here 41 is a prime number. Hence, 2^40/41 leaves a remainder 1. Thus, the remainder of ...

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Fermat Theorem

Find the rema...

Question

Find the remainder of $\frac{2^{41}}{41}$ ___

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Solution

We know that $A^{p - 1} \div p$ , leaves a remainder of 1, when p is a prime number.
Here 41 is a prime number. Hence, $\frac{2^{40}}{41}$ leaves a remainder 1. Thus, the remainder of $2^{41} \div 41$ would be equal to the remainder of $2^{1} \div 41 \to 2$ (required remainder)

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Find the remainder of 24141___

We know that Ap−1÷p, leaves a remainder of 1, when p is a prime number. Here 41 is a prime number. Hence, 24041 leaves a remainder 1. Thus, the remainder of 241÷41 would be equal to the remainder of 21÷41→2 (required remainder)

Find the remainder of $\frac{2^{41}}{41}$ ___

We know that $A^{p - 1} \div p$ , leaves a remainder of 1, when p is a prime number.
Here 41 is a prime number. Hence, $\frac{2^{40}}{41}$ leaves a remainder 1. Thus, the remainder of $2^{41} \div 41$ would be equal to the remainder of $2^{1} \div 41 \to 2$ (required remainder)