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.

#Algebra

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Comments

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

Daniel Liu - 7 years, 1 month ago

Degrees.

Sharky Kesa - 7 years, 1 month ago

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

Daniel Liu - 7 years, 1 month ago

@Daniel Liu – But is there proof?

Sharky Kesa - 7 years, 1 month ago

@Sharky Kesa – Proof of what? Doesn't supplying a counterexample suffice?

Daniel Liu - 7 years, 1 month ago

@Daniel Liu – 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.

Sharky Kesa - 7 years, 1 month ago

How can I post a problem??

Nick Batham - 7 years, 1 month 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

Finn Hulse - 7 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$