The oil in a lamp burns at a linear rate. The lamp contained 13 ounces of oil ten minutes after it was lit. It contained seven ounces of oil 38 minutes after it was lit. What was the original volume of oil before the lamp was lit?

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