[/quote]
,
such that 
.
be a function such that 
.
.
be positive integers and 
be prime. We know that 
and 
.
is a perfect square.
be a set of 
residues 
.
of of 
contains at least half of all the residues 
such that for all 
the following equality holds ![\[
f(\left\lfloor x\right\rfloor y)=f(x)\left\lfloor f(y)\right\rfloor \]](http://latex.artofproblemsolving.com/f/3/a/f3ac860e90d671f9fb592a6bd55c102a3000daec.png)
where 
is greatest integer not greater than 
of people, we define 
to be the least number of tables needed such that each person from the group sits in one of them with no two friends sitting on the same table, and 
to be the least number of tables needed such that each person from the group sits in one of them with no two enemies sitting on the same table.
such that for each group 
people we have![\[ f(n) \leqslant f(a(G)) + f(b(G)) \quad \text{and} \quad f(2) = 1.\]](http://latex.artofproblemsolving.com/0/3/d/03dfc700f9284152b39e32031c92c33283d65da6.png)
Find all possible values of 
.
is the set of all positive integers.
such that,
for all non-negative integers 
and 
.
is the set of all non-negative integers and 
is the set of all real numbers.
cells. It is said to be primitive it its cells cannot be partitioned into two or more dinosaurs. Find with proof the maximum number of cells in a primitive dinosaur.
cells is obtained by adjoining a new cell by making it adjacent to one or more existing cells.
Y by PikaPika999
I tried searching for myself in the AoPS User's list, and I didn't show up. I also tried scrolling through the posts leaderboard and I wasn't there either.
I tried searching some users, and it worked. For others, it didn't. Is there a reason why this search function is so inconsistent?
How to reproduce:
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I tried searching some users, and it worked. For others, it didn't. Is there a reason why this search function is so inconsistent?
How to reproduce:
try searching
pingpongmerrilyFollow this link https://artofproblemsolving.com/community/memberlist
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