Determining the degree of a polynomial

Asked Jul 23 '18 at 08:30

Active Jul 23 '18 at 12:12

Viewed 95 times

USAMO 1984:

"$P(x)$ is a polynomial of degree $3n$ such that

$P(0)=P(3)=\cdots =P(3n)=2$

$P(1)=P(4)=\cdots =P(3n-2)=1$

$P(2)=P(5)=\cdots =P(3n-1)=0$

$P(3n+1)=730.$

Determine $n$."

EDIT

This question already exists on the site, but the only answer given used the method of 'Lagrange interpolation', which I have not seen before. I'm fairly sure this problem should have a more elementary proof without using such a method. Instead, I've found this proof (https://mks.mff.cuni.cz/kalva/usa/usoln/usol845.html), which I don't really understand either. If someone could explain it to me that would be much appreciated.

edited Jul 23 '18 at 12:12

asked Jul 23 '18 at 08:30

Merk Zockerborg

What have you tried? Also, it would be nice if you could redact the problem in such a way that you don't portray yourself as demanding an answer. – qualcuno Jul 23 '18 at 08:40
The question has an answer on the site, you should try matlinks.ro aswell – asdf Jul 23 '18 at 08:47
1

Possible duplicate of Find "n" using the following conditions. – g.kov Jul 23 '18 at 09:23
thanks for the feedback, question has been edited – Merk Zockerborg Jul 23 '18 at 12:12
@GuidoA. I didn't make any noteworthy progress unfortunately – Merk Zockerborg Jul 23 '18 at 12:13
Check out a new recently added answer. – g.kov Jul 23 '18 at 16:52

Determining the degree of a polynomial

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