Question

-1 mod 19 please show work a =dq+r

Answer 1

The given expression can be written as -1=19(-1)+18.

Explanation:

According to quotient remainder theorem:

For any integer a and a positive integer d, there exist unique integers q and r such that

`a=d* q+r`

It can also written as

`a\text{mod }d=r`

The given expression is

`-1\text{mod }19`

Here a=-1 and d=19.

`(-1)/(19)=19(-1)+18`

`-1\text{mod }19=18`

If -1 is divides by 19, then the remainder is 18. The value of r is 18.

Therefore the given expression can be written as -1=19(-1)+18.