Question

When x is divided by 5, the remainder is 3. What is the remainder when 4x is divided by 4?

Answer 1

try with a number and see

Answer 2

or note that any number multiplied by 4 is a multiple of 4!

Answer 3

makes no difference what the remainder is when divided by any other number, \(4x\) is a multiple of \(4\) no matter what

Answer 4

x = 5*m + 3 where m is a Whole Number and greater than 3, but we do not actually need any of this information.

4 is always divisible by 4. Thus, 0.

Answer 5

Lets see.
When x/5= remainder =3
so when 4x/5= it is 4 times 3
divide 12 by 5, you get 2.

Answer 6

you are given x = 5k + 3, for some \[k \in Z\]

which is also written as x = 3(mod 5)
so 4x = 12(mod 5) => -x = 2(mod 5) => x = -2(mod5) => x=3

so the remainder for 4x/4 is
4x = 4k + r, for some \[k \in Z\], r = remainder

4x = r(mod 4)
r = 4x(mod 4) => r = 0x(mod4) so the remainder is r = 0x, \[\forall x \in Z \]