Monday, 3 November 2014

divisibility - Properties of Integers

A theorem presented in my discrete math book.




Let d be the smallest positive integer of the form ax+by.
Then d=gcd(a,b), where gcd means greatest common divisor.





I don't understand how the variable d being the smallest possible integer from the expression (ax+by) results in the greatest common divisor.



It also doesn't state what are the allowed values of a, b, x, and y are either.



My guess would be they want x and y to be integers.

No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...