Answer:
The given expression can be written as -1=19(-1)+18.
Step-by-step explanation:
According to quotient remainder theorem:
For any integer a and a positive integer d, there exist unique integers q and r such that
[tex]a=d\times q+r[/tex]
It can also written as
[tex]a\text{mod }d=r[/tex]
The given expression is
[tex]-1\text{mod }19[/tex]
Here a=-1 and d=19.
[tex]\frac{-1}{19}=19(-1)+18[/tex]
[tex]-1\text{mod }19=18[/tex]
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.
