Author(s)

Maoze Wang¹, Zhenxiang He², Meiyi Wang³

¹Lanzhou Institute of Technology, Lanzhou, China.
²School of Cyberspace Security, Gansu Politics and Law College, Lanzhou, China.
³Beijing Forestry University, Beijing, China.

Palindrome number conjecture: Take any non-palindromic natural number with two or more digits, add its inverse ordinal number, continue to use the inverted number of sum plus sum, repeat this process continuously. After a finite number of operations, a palindrome number must be obtained. We firstly give out several definitions: The pure-single-digit-of-sum is the number of single digits that only count the sum of two numbers of the same digit in the vertical operation of addition, which is referred to as pure single digit for short, denoted by g. The pure-carry-digit-of-sum is the carry digit that only counts the sum of two numbers in the same bit in the vertical operation of addition. It is a special number composed of only 1 and 0, which is represented by j'. The complement-0-carry-digit-of-sum is to supplement a 0 on the last side of j' according to the rule of adding bits, which is denoted by j. Therefore, in the addition operation, the sum of any natural number and its inverse ordinal number is divided into two parts: g and j. Then, the characteristics of g and j are characterized by the following two theorems: Theorem 1: As all the numbers in j are 0, j is the palindrome number; As the numbers in j are not all 0, j is not a palindrome number. Theorem 2: The sum of any palindrome number H and any non-palindrome j number must be a non-palindrome number. Then we proved the palindrome number conjecture is not correct by using the above two theorems.

Palindrome Number, Palindrome Number Conjecture, Inverse Number, Symmetry, Pure-Single-Digit, Pure-Carry-Digit, Complement-0-Carry-Digit

Wang, M. , He, Z. and Wang, M. (2022) The Deny Proof of the Palindrome Number Conjecture. Advances in Pure Mathematics, 12, 348-356. doi: 10.4236/apm.2022.124026.