Are there infinitely many integers $n, m$ such that $ϕ (n) = σ (m)$ ?

unreviewedOpen. Worked here; no verified result yet.

number theory · solved · formalized (Lean) · 0 attempts

machinery: totient-sigma-coincidence,prime-distribution,twin-primes,sieve/Brun-Titchmarsh,number-theory

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Formal proof

AMS 11 · solved (literature)

theorem erdos_48 :
    answer(True) ↔ {(n, m) : ℕ × ℕ | n.totient = σ 1 m}.Infinite

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