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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
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 …