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Topic: Looking for a polynpmial (Read 1540 times) |
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Mickey1
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Looking for a polynpmial
« on: Oct 18th, 2012, 2:30pm » |
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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?
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peoplepower
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Re: Looking for a polynpmial
« Reply #1 on: Oct 18th, 2012, 4:13pm » |
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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.
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| « Last Edit: Oct 18th, 2012, 4:54pm by peoplepower » |
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pex
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Re: Looking for a polynpmial
« Reply #2 on: Oct 19th, 2012, 3:18am » |
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Could you clarify what the difference is between this question and what you're asking in this thread?
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Mickey1
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Re: Looking for a polynpmial
« Reply #3 on: Oct 20th, 2012, 11:09am » |
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I am getting old. This is the same thing.
I must have been distracted.
Please disregard this.
I will answer in the other thread.
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