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Results tagged with algorithms
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user 2757
Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
15
votes
Variants of Waring's problem
Regarding question 1, it is easy to prove that $g'(k) \ge k$, and the expectation is that $g'(k)=k$ for all $k \ge 3$. But the equality is an open question even for $k=3$. See Deshouillers, Jean-Mar …
- 23.8k
7
votes
Lagrange four-squares theorem: efficient algorithm with units modulo a prime?
There is also an unconditional deterministic polynomial-time algorithm to find $x,y,z,w \in \mathbf{F}_p^\times$ such that $x^2+y^2+z^2+w^2=n$, given any $n \in \mathbf{Z}$ and any prime $p \ge 7$.
F …
- 23.8k
11
votes
Wants: Polynomial Time Algorithm for Decomposing a Multiset of Rationals into Two Additive S...
Any general algorithm for this problem will require exponential time. In fact, just writing down the answer can take exponential time in some cases.
For example, suppose that $n=2m$ for some odd $m$ …
- 23.8k