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

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

y=x+9

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step-by-step explanation: