Problems & Puzzles: Puzzles

Puzzle 1197 Follow up puzzle 282 In our Puzzle 282, Farideh Firoozbakh (†) asked these two questions: For non-palindromic solutions to the equation f(p)=f(p') where p is prime and p' is the reversible number about p, in two cases: f=φ f=σ where φ & σ  are the well known functions of the number theory, Euler function (φ) and Sum of divisors function (σ), respectively. Farideh found (August 28, 2004, date provided by G.L. Honaker, Jr.) none solution for the first case and only one solution for the second one (p=98639) Q. Can you give another try to this unsolved puzzle?

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Contributions from Nov 9 to Nov 15, came from Michael Branicky

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Michael wrote:

There are no solutions <= 10^10 for the first case (phi).

There are no solutions <= 10^10 other than the known 98639 for the second case (sigma).

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