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I want to do a division of two binaries and take the rest (mod). But I want to do this using polynomials, let's take the example:

binary dividend: 010001100101000000000000 binary divisor: 100000111

polynomial form dividend: $x^{22}+x^{18}+x^{17}+x^{14}+x^{12}$

polynomial form divisor: $x^8+x^2+x^1+x^0$

after the division: $\frac{x^{22}+x^{18}+x^{17}+x^{14}+x^{12}}{x^8+x^2+x^1+x^1}$

result is: $x^{14}+x^{10}+x^9+x^8+x^7+x^2+x^1$

Remainder is : $x^7+x^4+x^1$

Someone can explain to me, step-by-step, how to do this division? Without convert to binary, needs to be in polynomial form.

Thank you.

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