Palindrome Difference
Number Theory
Level
pending
Is it possible that a positive integer, subtracted by its palindrome, has a result that ends with 1?
For example: 1234 and 4321 are palindromes, but their difference is 3087, which ends with 7.
If Yes, give an example. If No, explain why is that so.
Yes
No
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1 solution
So, you want AB - BA = x1, where x can have as many digits as you want. Now, there are 2 cases, either:
B - A = 1, which means that B is greater than A, so A - B must be less than 0, which is obviously wrong, or
10 + B - A = 1, so 9 + B = A, A or B cannot be 0 as they are the leading digits of the palindromes, so this is obviously wrong.
Since both cases are impossible, then it means that it is impossible to get a result that ends with 1, so the answer is No.