Problems & Puzzles: Puzzles

Puzzle 282.  f(p) = f(p')

Faride Firoozbakht asks 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.

Faride has found none solution for the first case and only one solution for the second one (p=98639)


Find one (or one more) solution for each equation, argue that they are improbable, or show that they are impossible.

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