- #1
Bashyboy
- 1,421
- 5
Solve for x: 4x=6(mod 5)
Here is my solution:
From the definition of modulus, we can write the above as [itex]\frac{4x−6}{5}=k[/itex], where [itex]k[/itex] is the remainder resulting from [itex]4x~mod~5=6~mod~5=k.[/itex]
Solving for [itex]x[/itex], [itex]x=\frac{5k+6}{4}⟹x(k)=\frac{5k+6}{4}[/itex]
Now, my teacher said that is incorrect, and that [itex]k=...−2,−1,0,1,2,...[/itex]
I honestly don't understand what is wrong about my answer; and shouldn't k only take on nonnegative values, following from the definition of modulus?
Here is my solution:
From the definition of modulus, we can write the above as [itex]\frac{4x−6}{5}=k[/itex], where [itex]k[/itex] is the remainder resulting from [itex]4x~mod~5=6~mod~5=k.[/itex]
Solving for [itex]x[/itex], [itex]x=\frac{5k+6}{4}⟹x(k)=\frac{5k+6}{4}[/itex]
Now, my teacher said that is incorrect, and that [itex]k=...−2,−1,0,1,2,...[/itex]
I honestly don't understand what is wrong about my answer; and shouldn't k only take on nonnegative values, following from the definition of modulus?