if a|b and b|a, then a=b

am=b and bn=a but how do I show a=b?

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- June 17th 2010, 02:00 PMdwsmithif a|b and b|a, then a=b
if a|b and b|a, then a=b

am=b and bn=a but how do I show a=b? - June 17th 2010, 02:01 PMMoo
a/b=m and a/b=n, then...

- June 17th 2010, 02:05 PMdwsmith
- June 17th 2010, 02:09 PMAckbeet
am = b and bn = a implies a = (am)n = a(mn). What does mn have to be?

- June 17th 2010, 02:12 PMdwsmith
- June 17th 2010, 02:14 PMAckbeet
I think you can know more than that: a = a(mn) implies a (mn-1) = 0. Since a is not zero, mn - 1 = 0, which implies...

- June 17th 2010, 02:22 PMundefined
I'm assuming a and b are positive integers? Otherwise consider

a = 2

b = -2

If a and b are positive integers, then a|b implies a \le b and b|a implies b \le a, therefore a = b. - June 17th 2010, 03:20 PMmelese
- June 17th 2010, 03:37 PMundefined
Hmm, I'm not sure if this will display properly, I keep getting LaTeX errors on my previews.

Another way to get melese's result above is

Since this isn't rendering properly, here is an image I got using this site:

Attachment 17884 - June 19th 2010, 08:39 AMBruno J.