CMIIh

## Answered question

2021-07-31

$1=ax+by$, for all integers x and y
$1=ax+by$, for some integers x and y
$1=ax+by$, for unique integers x and y
All the above

### Answer & Explanation

au4gsf

Skilled2021-08-01Added 95 answers

Step 1
Two integers are relatively prime when there are no common factors other than 1. This means that no other integer could divide both numbers.
Two integers a,b are called relatively prime to each other if $gcd\left(a,b\right)=1$.
Step 2
For any positive integers a and b, there exist integers x andy such that $ax+by=gcd\left(a,b\right)$. Furthermore, as x and y vary over all integers a$x+by$ attains all multiples and only multiples of gcd(a, b).
Here $gcd\left(a,b\right)=1$
So there exist integers x and y such that $ax+by=1$
So the correct choice is b.
$1=ax+by$, for some integers x and y.

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