Erdős problem 418 · problems.science

Are there infinitely many integers not of the form $n - \phi(n)$ ?

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5 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

418.lean

Retained formal statement2 of 5

It follows from a slight strengthening of the Goldbach conjecture that every odd number can be written as $n - \phi(n)$ . In particular, we assume that every even number greater than 6 can be written as the sum of two *distinct* primes, in contrast to the usual Goldbach conjecture that every even number greater than 2 can be written as the sum of two primes.

FormalConjectures/ErdosProblems/418.leanErdos418.erdos_418.variants.conditional2 linesExact file

1(∀ (n : ℕ), 6 < n → Even n → ∃ p q, p ≠ q ∧ Nat.Prime p ∧ Nat.Prime q ∧ n = p + q) →2  ∀ (m : ℕ), Odd m → ∃ n, m + n.totient = n

SolvedStatement only, no proof

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