Let $x,y$ be distinct real numbers such that $\frac{x^n-y^n}{x-y}$ is an integer for $4$ consecutive positive integer $n$. Prove that $\frac{x^n-y^n}{x-y}$ is an integer for all positive integers $n$.
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zabachi123
30.06.2013 08:44
Sorry, is anyone able to help with this question?
lckihi
30.06.2013 09:12
zabachi123 wrote: Prove that $\frac{x^n-y^n}{x-y}$ is an integer for all positive integers $n$. Isn't this always true since $x-y \mid x^n-y^n$? Oh but, maybe the problem is $x$, $y$ may not be integer...
fattypiggy123
30.06.2013 11:20
https://www.artofproblemsolving.com/Forum/viewtopic.php?p=850133&sid=f1c3dee11f3495f52bdcaa2fd99e8f86#p850133
zabachi123
30.06.2013 11:49
Thanks, I cant believe the question in the contest is a repitition
SMOJ
30.06.2013 12:29
the junior Q4 is also a repetition