Help me with this random question.

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

"A sequence a1,a2,a3,...,ana_1, a_2, a_3, ..., a_n is defined by ai=100sin(i)a_i = \lfloor{100 \sin (i)}\rfloor where i=1,2,3,...,ni = 1, 2, 3, ..., n.

Is the expression

1+a1x+a2x2+...+anxn1 + 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
5 years, 1 month ago

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1 vote

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

Daniel Liu - 5 years, 1 month ago

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Degrees.

Sharky Kesa - 5 years, 1 month ago

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

Daniel Liu - 5 years, 1 month ago

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@Daniel Liu But is there proof?

Sharky Kesa - 5 years, 1 month ago

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

Daniel Liu - 5 years, 1 month 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 - 5 years, 1 month ago

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How can I post a problem??

Nick Batham - 5 years, 1 month 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 - 5 years, 1 month ago

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