,![\[\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}\geq 4+\frac{8(a-c)^2}{(a+b+c+d)^2}.\]](http://latex.artofproblemsolving.com/7/b/6/7b6e32d32d89ca058a06974e7276f0a5874d90a7.png)
such that the equation
be a positive integer and 
be a polynomial with integer coefficients such that 
.
is divisible by 
.
such that for every positive real 
,
satisfying![\[
\frac{\varphi(n!)}{n^\alpha\,(n-1)!} \;>\; c.
\]](http://latex.artofproblemsolving.com/4/4/4/4443cf7166cc65e67e2e504a826c4ac5f91aab2b.png)
Y by
Find the number of polynomials 
satisfying the following:
1.
;
2. the coefficients of are 
and 
;
3.
;
4.
has all of its coefficients being even.
Proposed by usjl
satisfying the following:1.
;2. the coefficients of
are 
and 
;3.
;4.
has all of its coefficients being even.Proposed by usjl
