An algebra problem by Anmol Jain

Algebra Level 3

IS THE FOLLOWING TRUE?

x^4 + x^3 + x^2 + x + 1 | x^44 + x^33 + x^22 + x^11 + 1.

WHERE ' | ' MEANS COMPLETELY DIVISIBLE WITH.

FALSE INSUFFICIENT INFORMATION DEPENDS ON VALUE OF X TRUE

1 solution

Vinayak Srivastava
May 23, 2020

I am waiting for someone to give a solution to this problem.

hint is try using complex number route, job will be done before u even know

Ruchir Singh - 1 month, 3 weeks ago

Thanks for the hint! I got it! Is there any more method?

Vinayak Srivastava - 1 month, 3 weeks ago

So setting $x^{44}+x^{33}+x^{22}+x^{11}+1 = p(x) (x^{4}+x^{3}+x^{2}+x^{1}+1 ) + q(x)$ where $\deg{(q(x))} \leq 3$ or $q(x)=0$ . Let $x^{4}+x^{3}+x^{2}+x^{1}+1 =0$ So we get $x^5=1$ . Then substituting in the original equation, we get $q(x)=0$ .

Vinayak Srivastava - 1 month, 3 weeks ago

Thank you @Ruchir Singh

Vinayak Srivastava - 1 month, 3 weeks ago

nice dude @Vinayak Srivastava

Ruchir Singh - 1 month, 3 weeks ago

An algebra problem by Anmol Jain

1 solution

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