The discussion revolves around defining the relation of divisibility between integers, specifically focusing on the greatest common divisor (gcd) and the lowest common multiple (lcm). Participants are exploring whether there exists an integer that divides every integer.
The discussion is ongoing, with various interpretations being explored. Some participants suggest that the integer 1 may be a candidate for dividing all integers, while others express uncertainty and question the original problem's intent.
There is a noted confusion regarding the interpretation of the original question, particularly concerning the types of numbers being considered (natural numbers versus integers). This has led to differing viewpoints on the existence of a universal divisor.
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...