The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Square roots of polynomials
Replies: 3   Last Post: Mar 25, 2014 4:59 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Jose Carlos Santos

Posts: 4,896
Registered: 12/4/04
Re: Square roots of polynomials
Posted: Mar 25, 2014 4:59 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 25-03-2014 7:00, quasi wrote:

>> Let P(x) be a polynomial with integer coefficients such that,
>> for each natural number _n_, P(n) is a perfect square. Does it
>> follow that P(x) is the square of some polynomial with integer
>> coefficients?

> Yes.
> My proof hinges on a key result which I call "The Sandwich
> Theorem". It's an elementary result, definitely known, but
> perhaps not well enough known.
> I independently discovered and proved this result when I was
> in high school.
> I'll state the theorem and some corollaries, without proof for
> now, but I'll supply proofs if requested.

Cute! Thanks a lot.

Best regards,

Jose Carlos Santos

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.