A number that will be the same when it is written forwards or backwards
is known as a Palindromic Number. For example, 1234321 is a palindromic
number. All single digit numbers are palindromic numbers.
Although palindromic numbers are most often considered in the decimal
system, the concept of palindromicity can be applied to the natural
numbers in any numeral system. Consider a number N > 0 in base b
>= 2, where it is written in standard notation with k+1 digits ai
as the sum of (ai
bi
) for i from 0 to k. Here, as usual, 0 <= ai
< b for all i and ak
is non-zero. Then N is palindromic if and only if ai
= ak-i
for all i. Zero is written 0 in any base and is also palindromic by definition.
Given any non-negative decimal integer N and a base b, you are supposed
to tell if N is a palindromic number in base b.