Given polynomials of degree n > 2, such that they have the form of(adsbygoogle = window.adsbygoogle || []).push({});

[itex]p(x) \ = \ x^n \ + \ a_1x^{n - 1} \ + \ a_2x^{n - 2} \ + \ a_3x^{n - 3} \ + \ ... \ + \ a_{n - 2}x^2 \ + \ a_{n - 1}x \ + \ a_n.[/itex]

[itex]And \ \ all \ \ of \ \ the \ \ a_i \ \ are \ nonzero \ integers \ (which \ you \ get \ to \ choose \ for \ each \ n).[/itex]

[itex]In \ \ terms \ \ of \ \ n, \ \ what \ \ is \ \ the \ \ greatest \ \ number \ \ of \ \ terms \ \ with [/itex]

[itex]\ \ coefficients \ \ that \ \ are \ \ zero \ \ that \ \ [p(x)]^2 \ \ can \ \ have \ ?[/itex]

[itex]Is \ \ it \ \ (n + 1) \ \ terms \ ?[/itex]

[itex]\text{Examples:}[/itex]

[itex](x^2 + 2x - 2)^2 \ = \ x^4 + 4x^3 - 8x + 4[/itex]

[itex](x^3 + 2x^2 - 2x + 4)^2 = x^6 + 4x^5 + 20x^2 - 16x + 16[/itex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Challenge to the community, Squaring of polynomials conjecture

**Physics Forums | Science Articles, Homework Help, Discussion**