The square-free palindrome conjecture in every base

Fix a base $b\geq 2$ and let $\overleftarrow{n}$ denote the integer obtained by reversing the base-$b$ digits of $n$. A square-free palindrome is a positive integer that is square-free and equal to its digital reverse. Square-free palindrome conjecture. For every base $b\geq 2$, there are infinitely many square-free palindromes; that is, infinitely many integers $n>0$ such that $n$ is square-free and $n=\overleftarrow{n}$. The paper presents this as a weakening of the palindromic-prime conjecture and as more approachable with current methods.