The discussion centers on defining the relation "a divides b" for integers a and b, alongside the concepts of greatest common divisor (gcd) and lowest common multiple (lcm). Participants clarify that the integer 1 is the only number that can evenly divide every integer, as it has the smallest absolute value. The conversation also highlights that no integer can divide every integer other than 1, reinforcing the uniqueness of this property.
PREREQUISITESStudents of discrete mathematics, educators teaching number theory, and anyone seeking to understand the foundational concepts of divisibility and integer relations.
HallsofIvy said:You are asked to find an integer that will evenly divide into every integer. First, in order that m divide n evenly, m cannot be bigger than n (in absolute value)! What is the smallest possible absolute value for an integer? What integers have that absolute value? Will they divide into every integer?
XodoX said:Homework Statement
Define the relation a I b ( a divides b) between integers a and b and then define the greatest common divisor, gcd ( a,b), and the lowest common multiple, lcm ( a,b) Is there any number for m for which you have n I m ( n divides by m) for every n.
I just found this one and I have no clue how to do it. It seems difficult to me. Can somebody please explain it to me?
HallsofIvy said:You are asked to find an integer that will evenly divide into every integer...