Problem 634 — Visual explainer (undergrad)
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Problem statement
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Find all $n$ such that there is at least one triangle which can be cut into $n$ congruent triangles.

Picture
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[Given objects + constraints]  --->  [Count / structure]  --->  [Show bound / existence]

Conjecture / Task: what to look at
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- Restate the problem as: given the constraint, what asymptotic bound or
  structure must follow?
- Use the comments as benchmarks (best known bounds / constructions).

Benchmarks / known results (from comments)
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- Soifer has shown that numbers of the form $2n^2,3n^2,6n^2,n^2+m^2$ also have
  this property.
- Beeson has shown (see the slides below) that $7$ and $11$ do not have this
  property.
- It is possible that any prime of the form $4n+3$ does not have this
  property.
- In particular, it is not known if $19$ has this property (i.e.