Question

: Find the remainder when 2^340is divided by 341
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Answer 1

Given:

$2^{340}$ is divided by 341.

To Find:

Remainder when $2^{340}$ is divided by 341.

Solution:

1) This is the case of the Fermat's theorem which states that if $\frac{a^{p-1}}{p}$ where p is prime number and a and p are co prime to each other then the remainder will be 1.

2) And here 341 is the prime number and 2 and p are co prime then,

Remainder for the term $\frac{2^{340}}{341}$ is 1.

Remainder when $2^{340}$ is divided by 341 is 1.

Answer 2

Answer:

answer 1

Step-by-step explanation:

Given:

2^{340}2

340

is divided by 341.

To Find:

Remainder when 2^{340}2

340

is divided by 341.

Solution:

1) This is the case of the Fermat's theorem which states that if \frac{a^{p-1}}{p}

p

a

p−1

where p is prime number and a and p are co prime to each other then the remainder will be 1.

2) And here 341 is the prime number and 2 and p are co prime then,

Remainder for the term \frac{2^{340}}{341}

341

2

340

is 1.

Remainder when 2^{340}2

340

is divided by 341 is 1.