Question

remainder when 2^123 is divided by 9
please answer ASAP
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Answer 1

Answer:

Which is the remainder of (2^123 + 3^121) when divided by 11?

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We need to compute remainder of (2^123 + 3^121) when divided by 11.

Step 1: Compute Euler phi for 11:

As 11 is prime number, so phi(11) = 11–1 = 10 as for primes, phi(p) = p-1

Step 2: Find the remainder of power using phi(11).

In 2^123, the power is 123. When 123 is divided by 10, the remainder is 3.

In 3^121, the power is 121. When 121 is divided by 10, the remainder is 1.

So, we need to compute (2^3 + 3^1).

2^3 + 3^1 = 8 + 3 = 11.

When 11 is divided by 11, the remainder is 0.

So, answer is 0.