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]

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# Challenge to the community, Squaring of polynomials conjecture

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