My answer to this was 6, but I have no solution because I just put some numbers in and played around with them. I'm wondering if it's possible to prove it using induction. Or if it's possible to solve it using modular arithmetic. Alternatively, another solution would be nice.
${g(x) = x^5 + x^4 + x^3 + x^2 + x + 1}$ What is the remainder when ${g(x^{12})}$ is divided by ${g(x)}$
1
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number-theory
polynomials
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0@SimplyBeautifulArt There's a missing constant term in your divisor polynomial. – 2017-02-04
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0@Deepak Oops. Nothing to see here! – 2017-02-04
1 Answers
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${\rm mod}\ g(x)\!:\ x^6\equiv 1\,\Rightarrow\, g(x^{12})\equiv g(1)\equiv 6$