What is the answer and remainder of 2^63 divided by 5 show work and also come up with a way to do it with a pattern of less than 10 digits. (try not to have it so complicated or long- needs to cover half a page)

Notice how 2^2 = 4 is one short of 5, so this means we can say 4/5 = 0 remainder 4 or we can write that "remainder 4" as "remainder -1" to say the same basic thing

Using modulus arithmetic, we can say...

2^2 = 4 = -1 (mod 5)

(2^2)^31 = (-1)^31 = -1 (mod 5)

2*(2^2)^31 = 2*(-1) (mod 5)

2^63 = -2 = 3 (mod 5)

So the remainder of 2^63 divided by 5 is the value 3

3

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.