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2
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Not especially famous, long-open problems which anyone can understand
Here are 2 problems related to cyclotomic polynomials that are unsolved :
Let $n,m>1$ and
$$A(x) = \Phi_n(x) + \Phi_m(x)$$
If $n,m$ are distinct odd primes then $A(x)$ is irreducible.
If $A(x)$ fact …