Question

When 425 is divided by prime number n, the remainder is 17, what is the remainder when 50 is divided by n ?

helpp pleaasseeee

Answer 1

Step-by-step explanation:

If 425 divided by a prime number n leaves a remainder of 17, we can write the equation 425 = n * q + 17, where q is some integer. If 50 is also divided by n with a remainder of r, we can write the equation 50 = n * s + r, where s is some integer.

Since 425 and 50 both leave the same remainder when divided by n, we can set these two equations equal to each other and solve for r:

425 = n * q + 17

50 = n * s + r

Subtracting 17 from both sides of the first equation gives us:

408 = n * q

Then subtracting 50 from both sides of the second equation gives us:

-8 = n * s - n

Adding n to both sides gives us:

0 = n * s

Since n is a prime number, it must be the case that s = 0. Therefore, r = 50.

So the remainder when 50 is divided by n is 50.