The palindromic decimal number N=abccba displays an interesting feature:
The value of abc in base 9 equals the value of cba in base 7.
What is N's prime factorization?
abc in base 9 equals cba in base 7 means
81a + 9b + c = 49c + 7b + a
40a + b = 24c
Since these must be numbers 0 to 6 its easy to check by hand. (I just tried each for c to see if it was close to or just under a multiple of 40.) The only solution is a=3, b=0, c=5.
N = 305503 = 11*27773
(11 is a factor of all palindromes with an even number of digits.)
Posted by Jer
on 2017-07-21 10:47:34