Reading the question can the product of four positive integers in A.P. be a square?, also made me question whether the product of $n$ positive integers, where $n \gt 5$ in arithmetic progression be a palindrome?
Me and user Peter tried to find solutions for various $n$ in PARI/GP, and found that there were no solutions for a large range of numbers we tested when $n \gt 5$.
This led to the following questions:
($1$) Can the product of $n$ positive integers, where $n \gt 5$ in A.P. be a palindrome?
($2$) If yes then for what value of $n$ is there no solution?