Determine n between 0 and 19 such that (2311)(3912) ≡ n mod 20.

You can write 2311 and 3912 in the form :

Then

Taken modulo 20, the terms containing powers of 20 vanish and you're left with

We further have

so we end up with

and so .

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If instead you're trying to find , you can apply Euler's theorem. We can show that using the Euclidean algorithm. Then since , and 8 divides 3912, we have

To show 2311 and 20 are coprime:

2311 = 115*20 + 11

20 = 1*11 + 9

11 = 1*9 + 2

9 = 4*2 + 1   =>  gcd(2311, 20) = 1

1,918

step-by-step explanation:

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step-by-step explanation: