,
is a digit. How many pairs of such numbers are there such that their sum is also a palindrome?
,
.
,
and 
.
is prime, 
with 
and 
w![$ \boxed{\ \left(\frac{n}{n+1}\right)^{n+1}<\sqrt [n+1]{(n+1) !}-\sqrt [n]{n!}\ }$](http://latex.artofproblemsolving.com/d/f/2/df2545bd7a1f1759e55190e60648d5cf65a2488a.png)
Y by Oksutok
Let ![$f(x)\in\mathbb Z[x]$](//latex.artofproblemsolving.com/2/9/5/2953d049559ec5d4020e6777d965bdfff9ebde0f.png)
have positive integer leading coefficient. Show that there exists infinte positive integer 
such that the number of digit that doesn'r equal to 
is no more than 
Created by Chunji Wang, Zhenyu Dong
![$f(x)\in\mathbb Z[x]$](http://latex.artofproblemsolving.com/2/9/5/2953d049559ec5d4020e6777d965bdfff9ebde0f.png)
have positive integer leading coefficient. Show that there exists infinte positive integer 
such that the number of digit that doesn'r equal to 
is no more than 
Created by Chunji Wang, Zhenyu Dong
