such that 
.
such that 
and 
.
.
such that the inequality below holds for any positive real numbers 
:![\[ \frac ab + \frac bc + \frac ca - 3 \geq k \left( \frac a{b + c} + \frac b{c + a} + \frac c{a + b} - \frac 32 \right).
\]](http://latex.artofproblemsolving.com/2/5/c/25c95e3e933649ed55bdd49ee446475223d8c871.png)
![$f \in R[X]$](http://latex.artofproblemsolving.com/b/5/6/b56c526a97b7f343d66e1317d98611980543ff21.png)
has an odd degree and it is given that 
is co-prime with 
and
Prove that 
there exists a positive integer N such that 
for every positive integer 
,
we denote the sum of digits of a positive integer 
.
be a sequence of rational numbers given by 
and for all 
we have 
.
can be partitioned into 
parallelograms. Prove that it can also be partitioned into 
parallelograms.
Y by
An integer 
is said to be a friendly integer if 
is not the square of an integer. Determine all integers 
such that there exists an infinite number of triplets of distinct friendly integers 
such that 
and 
is the square of an odd integer.
is said to be a friendly integer if 
is not the square of an integer. Determine all integers 
such that there exists an infinite number of triplets of distinct friendly integers 
such that 
and 
is the square of an odd integer.This post has been edited 1 time. Last edited by parmenides51, May 9, 2021, 9:56 PM
