Prime divisors of palindromes

Author： Banks William D.   Shparlinski Igor E.  

Publisher： Springer Publishing Company

ISSN： 0031-5303

Source： Periodica Mathematica Hungarica, Vol.51, Iss.1, 2005-11, pp. : 1-10

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Abstract

In this paper, we study some divisibility properties of palindromic numbers in a fixed base ]]>]]>]]>]]>]]>]]>]]>]]>gge 2$. In particular, if ${mathcal P}_L$ denotes the set of palindromes with precisely $L$ digits, we show that for any sufficiently large value of $L$ there exists a palindrome $nin{mathcal P}_L$ with at least $(loglog n)^{1+o(1)}$ distinct prime divisors, and there exists a palindrome $nin{mathcal P}_L$ with a prime factor of size at least $(log n)^{2+o(1)}$.

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