#math-immediate
TAOCP 1.2.4 Exercise 13
Section 1.2.4: Integer Functions and Elementary Number Theory Exercise 13. [ M00 ] By convention, we say that the greatest common divisor of 0 and $n$ is $|n|$. What integers are relatively prime to 0? Verified: yes Solve time: 2m22s By convention, $\gcd(0,n)=|n|$. Two integers are relatively prime if their greatest common divisor is $1$. Therefore an integer $x$ is relatively prime to $0$ if and only if $$ \gcd(x,0)=|x|=1....
TAOCP 1.2.3 Exercise 17
Section 1.2.3: Sums and Products Exercise 17. ▶ [ M00 ] Let $S$ be a set of integers. What is $\sum_{j \in S} 1$? Verified: yes Solve time: 34s By definition, $\sum_{j \in S} 1$ is the sum of one copy of $1$ for each integer $j$ belonging to $S$. Therefore the value of the sum is simply the number of elements of $S$. If $S$ is finite, containing exactly...