Question 1019846: The numbers 13 and 31 is the reverse of the other, and their squares have the same property.Prove that there are infinite natural numbers which one is the reverse of the other one, and their squares have the same property.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! The question (as you asked it) allows for a really cheap solution - just take all integers of the form 1, 11, 101, 1001, 10001, etc. They are palindromes, so the reverse is the same. Also, their squares are palindromes, and this is easy to show in general.
If the pairs must consist of *distinct* positive integers (such as (13,31)), then the following construction also works:
(13,31) = (11+2, 11+20)
(103,301) = (101+2, 101+200)
(1003,3001) = (1001+2, 1001+2000)
etc.
since each of the squares is equal to 10...060...9 and 90...060...1 respectively.
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