Question

when the positive integer x is divided by 11, the quotient is y and the remainder 3. when x is divided by 19, the remainder is also 3. what is the remainder when y is divided by 19?

Answer 1

A.T.Q.
X=11y+3
also X=19z+3, let z be an arbitrary number
that implies
11y=19z
that implies
y=19z/11
when y is divided by 19,we get
y/19=19z/11/19=z/11
it leaves no remainder
so the answer is 0.