id: 00090584
dt: j
an: 00090584
au: Korec, Ivan
ti: Palindromic squares for various number system bases.
so: Math. Slovaca 41, No.3, 261-276 (1991).
py: 1991
pu: Mathematical Institute of the Slovak Academy of Sciences, Bratislava;
    Versita, Warsaw; Springer, Heidelberg
la: EN
cc: 
ut: palindromic numbers; number system; reciprocal polynomial
ci: 
li: 
ab: A positive integer $y$ is called a $b$-adic palindrome $(b>1)$ if its
    $b$-adic expansion $y=c\sb n c\sb{n-1}\dots c\sb 0$ (without any
    leading zero digits) satisfies $c\sb i=c\sb{n-i}$ for all
    $i=0,1,\dots,n$. If $y$ is a square, $\sqrt{y}=a\sb n a\sb{n-1}\dots
    a\sb 1a\sb 0$ (with leading zeros if necessary) and $\sum\sb{k=0}\sp i
    a\sb k\cdot a\sb{i-k}=c\sb i$ for all $i=0,1,\dots,n$, then we say $y$
    is a trivial $b$-adic palindromic square. The author shows polynomials
    whose values produce nontrivial $b$-adic palindromic squares and proves
    that there are infinitely many $b$-adic nontrivial palindromic squares
    for any $b>2$. The problem that remains open: Are there infinitely many
    palindromic squares for the base $b=2$?
rv: P.Kiss (Eger)