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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
3 years, 9 months ago

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

Daniel Liu - 3 years, 9 months ago

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Degrees.

Sharky Kesa - 3 years, 9 months ago

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

Daniel Liu - 3 years, 9 months ago

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@Daniel Liu But is there proof?

Sharky Kesa - 3 years, 9 months ago

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

Daniel Liu - 3 years, 9 months ago

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@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 - 3 years, 9 months ago

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How can I post a problem??

Nick Batham - 3 years, 9 months ago

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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 - 3 years, 9 months ago

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