Suppose a set
satisfies the following conditions:-
(1) every element in
is a positive integer and not greater than
,
(2) for any two different elements
and
in
, there is an
element
in
such that the greatest common divisor of a and
is equal to
, and the greatest common divisor of b and c is
also 1; and
(3) for any two different elements
and
in
, there is an
element
, which is different from
and
, such that the
greatest common divisor of
and
, and that of
and
are
greater than 1.
Find the maximum number of elements in
.
ANSWER
thank u
by kabi, Sep 03, 2009, 6:18 am 
and 
is differentiable function satisfies :
then find 
and {
} = {
} = {
}where {
} =
![x- [x]](http://data.artofproblemsolving.com/images/latex/b/7/3/b73e9ed2b263a29ac98a3c2f8cb876bc9be6dceb.gif)
and ![[x]](http://data.artofproblemsolving.com/images/latex/3/c/3/3c345a8aed30f94cb97f496efca2e4209abad676.gif)
denotes the integral part of the number x. Find
, 
,
which is continuous for 
and 
,then for 
belongs to ![[c,d]](http://data.artofproblemsolving.com/images/latex/9/1/a/91aa029d208f02c60677076dd11d78bd0c8dc3cc.gif)
and we need to find
September 2009
July 2009
