Conjecture Let if is odd and if is even. Let . Assume we start with some number and repeatedly take the of the current number. Prove that no matter what the initial number is we eventually reach .
The zeroes of the Riemann zeta function that are inside the Critical Strip (i.e. the vertical strip of the complex plane where the real part of the complex variable is in ]0;1[), are actually located on the Critical line ( the vertical line of the complex plane with real part equal to 1/2)
Conjecture Let be the space of Diffeomorphisms on the connected , compact and boundaryles manifold M and the space of vector fields. There is a dense set ( ) such that exhibit a finite number of attractor whose basins cover Lebesgue almost all ambient space
This is a very Deep and Hard problem in Dynamical Systems . It present the dream of the dynamicist mathematicians .
Conjecture For , let be the statement that given any exact -coloring of the edges of a complete countably infinite graph (that is, a coloring with colors all of which must be used at least once), there exists an exactly -colored countably infinite complete subgraph. Then is true if and only if , , or .
Conjecture There exists a fixed constant so that every abelian group has a subset with so that the Cayley graph has no clique or independent set of size .
Problem Consider the set of all topologically inequivalent polyhedra with edges. Define a form parameter for a polyhedron as where is the number of vertices. What is the distribution of for ?
Conjecture Let be a simple -uniform hypergraph, and assume that every set of points is contained in at most edges. Then there exists an -edge-coloring so that any two edges which share vertices have distinct colors.
Conjecture For all there is an integer such that every digraph of minimum outdegree at least contains a subdivision of a transitive tournament of order .
Problem Is there an algorithm which takes as input a triangulated 4-manifold, and determines whether or not this manifold is combinatorially equivalent to the 4-sphere?
Question Can either of the following be expressed in fixed-point logic plus counting: \item Given a graph, does it have a perfect matching, i.e., a set of edges such that every vertex is incident to exactly one edge from ? \item Given a square matrix over a finite field (regarded as a structure in the natural way, as described in [BGS02]), what is its determinant?
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, every (loopless) graph 
with 
immerses 
. 
if 
is odd and 
if 
. Assume we start with some number 
of the current number. Prove that no matter what the initial number is we eventually reach 
. 
-
(mod 
) for every vertex 
. 
be the flow polynomial of a graph 
, the value 
equals the number of 
for every 2-edge-connected graph 
are simple finite graphs, then 
. 
is the 
.
, it is impossible to cover a square of side greater than 
unit squares. 
be the space of 
Diffeomorphisms on the connected , compact and boundaryles manifold M and 
the space of 
(
) such that 
exhibit a finite number of attractor whose basins cover Lebesgue almost all ambient space 
, let 
be the statement that given any exact 
-coloring of the edges of a complete countably infinite graph (that is, a coloring with 
-colored countably infinite complete subgraph. Then 
, 
, or 
.
so that every abelian group 
with 
so that the 
has no clique or independent set of size 
. 
? ![$ p \in {\mathbb Q}[x] $](/files/tex/a72fcb0a006c3c2afb3ba69722ccdb2599b83e90.png)
rationally derived if all roots of 
and the nonzero derivatives of 
, the 
, is defined as the sum of all 
by using partitions. 
-flow 
on 
of 
from the edge set of 
, for all 
, and 
.
-regular graph 
for every 
with 
odd.
be an integer. If 
. 
where 
for 
? 
-
points is contained in at most 
-edge-coloring so that any two edges which share 
such that every digraph of minimum outdegree at least 
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