n variable polynomial + /-if the number of $-1$'s is even, or odd, respectively. Prove that the degree of this polynomial is at least $n$.

Asked Mar 23 '16 at 04:36

Active Mar 23 '16 at 04:36

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Consider a polynomial in $n$ variables with real coefficients. We know that if every variable is $\pm1$, the value of the polynomial is positive, or negative if the number of $-1$'s is even, or odd, respectively. Prove that the degree of this polynomial is at least $n$.

n variables make the polynomial more interesting

asked Mar 23 '16 at 04:36

What's the source of this question, please? – Gerry Myerson Mar 23 '16 at 06:02
I got this problem from AoPs – Mar 23 '16 at 14:51
URL, please, so we can all join in the fun? – Gerry Myerson Mar 23 '16 at 22:36
1

https://www.artofproblemsolving.com/community/u257453h1213005p6022786 – Mar 24 '16 at 06:31
Too bad the person who put it on AoPS didn't give any information about it. – Gerry Myerson Mar 26 '16 at 11:56

n variable polynomial + /-if the number of $-1$'s is even, or odd, respectively. Prove that the degree of this polynomial is at least $n$.

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