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.

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