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using the fact that : A positive integer n ≥ 3 is constructive if it is...

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Advance Math

using the fact that : A positive integer n ≥ 3 is constructiveif it is possible to construct a regular n-gon by straightedge andcompass, it is possible to construct the angle 2π/n. And that ifboth angles α and β can be constructed by straightedge and compassthen so are their sums and differences.The outside angle of aregular n-gon is 2π/n.

1. Suppose that n = p^(α1) ··· p^(αk) where p ,··· , pk aredistinct odd primes. Prove that n is constructive if and only ifeach pi^(αi) is constructive.

2. Prove that 2^α is constructive for any positive integer α ≥2

Answer & Explanation Solved by verified expert
4.0 Ratings (638 Votes)
1 np1a1pkak where p1pk are distinct odd primes Let i be any of 12k Then np1a1pi1ai1pi1ai1pkakpiaixpiai where x is a positive integer I shall denote pi by pi Then 2pin2pixpiai 2pipiai2xpin Let us suppose that n is constructive Then it is possible to construct the angle 2pin by straightedge and compass Now it has been said that sums of constructible angles are also constructible then positive integer    See Answer
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