andreis

Hm, still no solution. It's supposed to be a school problem.

The Python code returns the smallest palindrome P given an integer p (num in the code).

import sys
def is_palindrome(num):
if (num % 10 == 0):
return False;
r = 0;
while (r < num) :
r = 10 * r + num % 10;
num /= 10;
return (num == r) or (num == r / 10);
num = input("Enter a positive integer:");
k=0;
multiple=12;#initialisation: any non-palindrome
while (not is_palindrome(multiple)):
k+=1;
multiple=k*num;
print(str(num)+"*"+str(k)+"="+str(multiple));

Hi Function,

Your formula doesn't work for odd numbers. The digit in the middle will have the number (n+1)/2, and you will have a sum member 2*x_i*10^{(n-1)/2} instead of x_i*10^{(n-1)/2}.

I made a similar decomposition, but could not get any conclusion from it.

Let's be more specific, palindromicity is checked in decimal system. Corrected above.