Timeline for Prove by induction that $x^n-y^n$ is divisble by $x-y$ for $ n \ge 1 $

8 events

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May 19, 2018 at 8:22	comment	added	Mr Pie		@J.G. thank you for showing me that post in the link. It is very interesting. I wonder if there are any other assertions that cannot be proven without induction :)
May 19, 2018 at 8:20	comment	added	J.G.		I don't think so. I'm sure someone would suggest "use the factor theorem", but the proof of that probably requires induction on the degree of polynomials. My favourite on-SE discussion of what constitutes induction is math.stackexchange.com/a/1359020
May 19, 2018 at 8:14	history	edited	Mr Pie	CC BY-SA 4.0	added 19 characters in body
May 19, 2018 at 8:13	comment	added	Mr Pie		@J.G. hah... I didn't realise. Looks like it is an inductive proof. Is there a way of proving the assertion with-out the use of induction, do you know?
May 19, 2018 at 8:11	comment	added	J.G.		"It terminates like this" is your inductive hypothesis.
May 19, 2018 at 8:08	comment	added	Mr Pie		@J.G. what do you mean? I have not used a base case, inductive hypothesis, or an inductive step. I just cleverly rewrote the numerator.
May 19, 2018 at 8:05	comment	added	J.G.		That's still induction.
May 19, 2018 at 7:43	history	answered	Mr Pie	CC BY-SA 4.0