- #1
ninjagod123
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I am starting Number Theory this semester. My professor hands out notes but there is no textbook for the class. So hopefully you guys can help me with these seemingly easy problems.
Z = {...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...}
Z is used to denote the set of integers
1) Show that if a is an element of Z and 0< a, then 1<=a
2) Let a and b be integers. Let us say that a divides b if there is an integer c such that b = ac. Show that if b>0 and a divides b then a<=b.
All we have learned so far are basic arithmetic properties, the Well-Ordering Principle, and the Induction Principle.
Z = {...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...}
Z is used to denote the set of integers
1) Show that if a is an element of Z and 0< a, then 1<=a
2) Let a and b be integers. Let us say that a divides b if there is an integer c such that b = ac. Show that if b>0 and a divides b then a<=b.
All we have learned so far are basic arithmetic properties, the Well-Ordering Principle, and the Induction Principle.