Suppose the quotient of two odd integers is an integer. Make and prove a conjecture about whether the quotient is either even or odd.
If you had an even (2n) divided by and odd (2m+1), it wont work. so my odd integers would be a= 2n+1 and b=2m+1
a/b = c = (2n+1)/(2m+1) which is also odd so c = (2w + 1)
c|a, so a = [(2n+1)/(2m+1)] * k for some integer k
????? or I have
Let a = 2n +1 and b = 2m + 1. From the definition a/b = c and c|a, then we get a/b = c . Thus a = b*c = (2m+1)(c) = 4mc + c = c(4m + 1). Then, we have an equation that is (c)*(odd) making the final result odd.
examples: 9/3 = 3 21/7 = 3 81/9 = 9 49/7 = 7 35/5 = 7