# Help me with this random question.

I had been making questions I wanted to try on myself and decided to do this.

"A sequence $a_1, a_2, a_3, ..., a_n$ is defined by $a_i = \lfloor{100 \sin (i)}\rfloor$ where $i = 1, 2, 3, ..., n$.

Is the expression

$1 + a_1x + a_2x^2 + ... + a_nx^n$

factorable or irreducible and give proof."

I am pretty sure it is irreducible but could not give proof. I thought I could ask Brilliant to help me find a proof. Note by Sharky Kesa
6 years, 7 months ago

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How can I post a problem??

- 6 years, 7 months ago

Locate the "Post" button located to the right of the "Practice" button, which in turn is to the right of the "Home" button. There should be a little green $+$-sign. Click on this, and select "Problem". Then, you're free to write any problem you want. Enjoy! :D

- 6 years, 7 months ago

Is the $i$ inside $\sin (i)$ supposed to be in radians or degrees?

- 6 years, 7 months ago

Degrees.

- 6 years, 7 months ago

In that case, I believe that it can be factorable for certain $n$. For example, $n=719$, if my intuition is correct.

- 6 years, 7 months ago

But is there proof?

- 6 years, 7 months ago

Proof of what? Doesn't supplying a counterexample suffice?

- 6 years, 7 months ago

Does it only happen with 719 or is there a rule for the values of n for which it is factorable or irreducible? That sort of proof.

- 6 years, 7 months ago