wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> medium >> Looking for a polynpmial 
        
(Message started by: Mickey1 on Oct 18^th, 2012, 2:30pm)

Title: Looking for a polynpmial
Post by Mickey1 on Oct 18^th, 2012, 2:30pm

I wonder for reasons related to Pell’s equation whether

For any non-constant polynomial P1(n) with natural number coefficients , there exists another similar non-constant polynomial P2(n) so that P1(P2(n))=(P(n))^2?

Title: Re: Looking for a polynpmial
Post by peoplepower on Oct 18^th, 2012, 4:13pm

I am sure the general solution is not very scary, but a smallest case might be:
P1(x)=x, where P2(x) shall be any square.
P1(x)=x^2, in which case P2(x) may be any (non-constant, as you require) polynomial.

However, the derivation of the general solution may be a bit frightening. We essentially have to have a sum, which is over specific partitions of various integers giving powers of the "given" coefficients, to be divisible by a certain binomial coefficient.

Title: Re: Looking for a polynpmial
Post by pex on Oct 19^th, 2012, 3:18am

Could you clarify what the difference is between this question and what you're asking in this thread (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1350593416)?

Title: Re: Looking for a polynpmial
Post by Mickey1 on Oct 20^th, 2012, 11:09am

I am getting old. This is the same thing.
I must have been distracted.

Please disregard this.
I will answer in the other thread.