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Results tagged with open-problems
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user 2757
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?"
294
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8
answers
22k
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Polynomial representing all nonnegative integers
Lagrange proved that every nonnegative integer is a sum of 4 squares.
Gauss proved that every nonnegative integer is a sum of 3 triangular numbers.
Is there a 2-variable polynomial $f(x,y) \in \math …
- 23.8k
24
votes
Are most cubic plane curves over the rationals elliptic?
Your question (as explained in the second paragraph) is not vague at all! In fact, it appears for instance after Conjecture 2.2 in http://www-math.mit.edu/~poonen/papers/random.pdf , which is Random …
- 23.8k
20
votes
Irreducible polynomials with constrained coefficients
Your problem is hard, but here are some things that can actually be proved!
Let $S_d$ be the set of polynomials of degree $d$ with all $d+1$ coefficients in $\{\pm 1\}$.
1) $|S_d| \gg 2^d/d$ as $d \ …
- 23.8k
12
votes
Accepted
distribution of degree of minimum polynomial for eigenvalues of random matrix with elements ...
The survey article
Jason Fulman, Random matrix theory over finite fields, Bulletin of the AMS 39 (2002), 51-85
and the references therein should answer your questions to the extent that the answers …
- 23.8k