Write a complete mathematical definition of (a,b), the greatest common divisor of a,b in \mathbb{Z}

Answer:The greatest common divisor of two integers a and b (not both 0) is the largest integer that divides both a and b.Step-by-step explanation:Think for example of the numbers a=5, and b= -10. The greatest common divisor of 5 and -10, is the largest integer that divides both 5 and -10. We can find it by inspection (although there are more advanced methods to find it). We can list all integers that divide both 5 and -10.-5 divides 5, and it also divides -10-1 divides 5, and it also divides -101 divides 5, and it also divides -105 divides 5, and it also dividies -10The LARGEST of them all is then 5, so 5 is the greatest common divisor of 5 and -10. The usual way to write it is[tex]gcd(5,-10)=(5,-10)=5[/tex]