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Mystery number

in
Hindu-Arabic numerals: much loved and indispensable.

Find the number $x$ that satisfies these two properties:

  • The digits of $x$ add up to a number $y$ where $x$ equals $y$ times the number you get when you reverse the digits of $y$.
  • Reverse the digits of $x$ and find the prime factors of the number you get. Then take the sum of the squares of these prime factors and halve it. Removing the digit 0 from the new number yields back $x$.

Here's a hint.



This puzzle was contributed by Aziz Inan, Professor of Electrical Engineering at the University of Portland. He chose it in honour of a famous mathematician who would have turned 125 this year.

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