TAOCP 1.2.4 Exercise 12
Every integer $x$ is divisible by 1, since $x = 1 \cdot x$.
Section 1.2.4: Integer Functions and Elementary Number Theory
Exercise 12. [00] What integers are relatively prime to 1?
Verified: yes
Solve time: 2m56s
Every integer $x$ is divisible by 1, since $x = 1 \cdot x$. Therefore the greatest common divisor of 1 and $x$ is $\gcd(1,x) = 1$ for all integers $x$. By definition, two integers are relatively prime if their greatest common divisor is 1. Hence every integer is relatively prime to 1. This completes the proof. ∎
$$ \boxed{\text{All integers are relatively prime to 1.}} $$