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That helps clear it up even further. Thank you!
Thanks a lot for your quick response! That definitely makes it clearer to me. However, should that conclusion ("if m and n are both a multiple of some number, then m-qn must be a multiple of that number as well") be obvious? (Without working out the steps, I mean.) I am (obviously) not naturally good with math (despite having taken all honors math classes in high school, as well as Calculus in college). So how the second part of that statement flows from the first is not obvious to me. Is it just my rusty math skills that make this not obvious, or is the reader just meant to take the author's word for it that the statement is true. I guess I'm just asking for an opinion on this.
Thanks again!
Hi,
I'm working through a computer science book and at one point the author says this:
"After step E1, we have m = qn + r, for some integer q. If r <> 0, note that any number that divides both m and n must divide m - qn =r and any number that divides both n and r must divide qn + r = m."
I don't understand the terminology here. I mean, I understand that you can subtract qn from both sides and get m - qn = r, and I understand that qn + r = m is the same thing as m = qn + r. But what does it mean to say that a number "divides" a whole equation? What do "must divide m - qn = r" and "must divide qn + r = m" mean? Thanks in advance for any help.
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