Erdős problem 11 · problems.science

Is every odd $n > 1$ the sum of a squarefree number and a power of 2?

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6 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

11.lean

Retained formal statement4 of 6

Suppose that every odd $n$ is the sum of a squarefree number and a power of 2. Then the set of primes $p$ such that $2 ^ p ≡ 2 \mod p ^ 2$ is infinite. This is Theorem 1 in [GrSo98]. [GrSo98] Granville, A. and Soundararajan, K., A Binary Additive Problem of Erdős and the Order of $2$ mod $p^2$ . The Ramanujan Journal (1998), 283-298.

FormalConjectures/ErdosProblems/11.leanErdos11.erdos_11.variants.granville_soundararajan1 lineExact file

1(∀ (n : ℕ), Odd n → 1 < n → ∃ k l, Squarefree k ∧ n = k + 2 ^ l) → {p | Nat.Prime p ∧ 2 ^ p ≡ 2 [MOD p ^ 2]}.Infinite

SolvedStatement only, no proof

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