If a divided by 4 leaves a remainder of 2 and b divided by 4 leaves a remainder of 3, then when a + b is divided by 4, the remainder is
A. 0 B. 1 C. 2 D. 3 E. 4
Let all letters represent non-negative integers with
If divided by gives quotient and remainder , then
Conversely, if and , then divided by
gives quotient and remainder .
Suppose divided by gives quotient and
suppose divided by gives quotient , then
Adding the two equations,
Write as
By the converse above, divided by gives quotient
and remainder .
That's choice b.
Edwin