Let us consider a number, e.g. 1234
Now reverse the positions of the terminal digits, so we get 4231
4231-1234=2997 which is divisible by 9
i have seen this for n-digit numbers, where n ranges from 2 to 6
Is there any number which is contradicting this behavior irrespective of its number of digits?
Now coming back to the example,
Now 2997/9=333 is a palindrome
Another example 923456781-123456789=799999992
Is this also independent of the number of digits of the original number?
Let us consider :
The largest prime factor of 6666 is 101 which is a palindrome and a prime number.
Again 66/11(11 being the largest prime factor of 66) equals to 6 which is a palindrome.
Another example :
The largest prime factor of 88888888 is 137
88888888/137=648824/101(101 being largest prime factor of 648824)=6424/73(73 being largest prime factor of 6424) this in turn equals to 88 (a palindrome)
Finally, 88/11(11 being largest prime factor of 88 and a palindrome) equals to 8 which is also a palindrome.
Now as per (http://math.stackexchange.com/questions/200835/are-there-infinitely-many-super-palindromes), will it be correct to call 88888888 a super palindrome?
Can it be possible to call a number a super palindrome if it generates non palindromes along with palindromes, provided the non-palindromes finally generate using the method of division by largest prime factor, a palindrome other than 1?