1. ## The Division Algorithm

The Division Algorithm states: Let a,b belong to Z, b does not equal zero. Then there exist unique integers q and r, with 0 is less than or equal to r and less then the absolute value of b, such that a = qb+r

I have a question here that asks: Find q and r as defined in the Division Algorithm in each of the following cases:

i) a = 5286; b = 19
ii) a = -5286; b = 19
iii) a = 5286; b = -19
iv) a = 19; b = 5286

Any help with any of these would be greatly appreciated. Thanks a lot guys.

2. Originally Posted by GreenDay14
The Division Algorithm states: Let a,b belong to Z, b does not equal zero. Then there exist unique integers q and r, with 0 is less than or equal to r and less then the absolute value of b, such that a = qb+r

I have a question here that asks: Find q and r as defined in the Division Algorithm in each of the following cases:

i) a = 5286; b = 19
ii) a = -5286; b = 19
iii) a = 5286; b = -19
iv) a = 19; b = 5286

Any help with any of these would be greatly appreciated. Thanks a lot guys.
There are many ways to find this. Merely note that $\displaystyle q=\left\lfloor\frac{a}{b}\right\rfloor$ where $\displaystyle \left\lfloor .\right\rfloor$ is the floor function. and $\displaystyle r$ is just $\displaystyle a\text{ mod }b$. Or if your aren't familiar with that notation, let $\displaystyle {x}$ be the "fracional part" of $\displaystyle x$. Then $\displaystyle r=b\cdot\left\{\frac{a}{b}\right\}$