Problems & Puzzles: Puzzles

Puzzle 330. σ(φ(σ(p)))=φ(σ(φ(p))) Faride Firoozbakht poses the following puzzle: Prove the following statement or find a counter example. "Every prime p such that σ(φ(σ(p)))=φ(σ(φ(p))) is of the form 4k+1"

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Contributions came from Joseph L. Pe.

Joseph wrote:

Here is a counterexample to the conjecture proposed in puzzle #330:

The prime p = 114190259 = 4 * 28547564 + 3 is of the form 4x + 3,

and

 

sigma(phi(sigma(p))) = phi(sigma(phi(p))) = 63452160.

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