Prove that 1 and -1 are only divisible by 1 and -1.
I think that I'm making this too complicated. Any help would be greatly appreciated.
I do it with , do it for .
A number is divisible by a number if and only if with .
It's obvious that .
So in your case you have that . That means that if was divisible by a number , it would necessarily be . We can try to check if it works : , which works.
I think what I did is not wrong...
Good luck. (All you have to do is to generalize what I did for the numbers for any number . I suggest you to check this : Division algorithm - Wikipedia, the free encyclopedia out.)
The division algorithm just says that given and , there exists a unique and , such that . Doesn't mention about a dividing b or vice versa but we can see that b divides a when r = 0.
For this question, just go by definition:
If , we have that the numerator is less than the denominator which cannot be an integer. Thus . So must be ...