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Omni-MATH / Our third and final item comes to us from Germany, I mean Geometry. It is known…

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Our third and final item comes to us from Germany, I mean Geometry. It is known that a regular nn-gon can be constructed with straightedge and compass if nn is a prime that is 1 plus a power of 2. It is also possible to construct a 2n2 n-gon whenever an nn-gon is constructible, or a p1p2⋯pmp_{1} p_{2} \cdots p_{m}-gon where the pip_{i} 's are distinct primes of the above form. What is really interesting is that these conditions, together with the fact that we can construct a square, is that they give us all constructible regular nn-gons. What is the largest nn less than 4,300,000,0004,300,000,000 such that a regular nn-gon is constructible?
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Our third and final item comes to us from Germany, I mean Geometry. It is known that a regular n-gon can be constructed with straightedge and compass if n is a prime that is 1 plus a power of 2. It is also possible to construct a 2n-gon whenever an n-gon is constructible, or a p₁p₂⋯p_(m)-gon where the p_(i) 's are distinct primes of the above form. What is really interesting is that these conditions, together with the fact that we can construct a square, is that they give us all constructible regular n-gons. What is the largest n less than 4,300,000,000 such that a regular n-gon is constructible?
Original LaTeX notation
Our third and final item comes to us from Germany, I mean Geometry. It is known that a regular $n$-gon can be constructed with straightedge and compass if $n$ is a prime that is 1 plus a power of 2. It is also possible to construct a $2 n$-gon whenever an $n$-gon is constructible, or a $p_{1} p_{2} \cdots p_{m}$-gon where the $p_{i}$ 's are distinct primes of the above form. What is really interesting is that these conditions, together with the fact that we can construct a square, is that they give us all constructible regular $n$-gons. What is the largest $n$ less than $4,300,000,000$ such that a regular $n$-gon is constructible?

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task_id
c7cb241a-1d25-563a-a177-ed5fd62b87ae
task_key
test--c7cb241a-1d25-563a-a177-ed5fd62b87ae
task_revision_id
1
config / split
/ test

Official source

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