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Erdős problem 700

f n is a lower bound: f n ≤ gcd(n, C(n,k)) for every 1 < k ≤ n/2.

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The source's own material, retained exactly.

9 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

700.lean

Retained formal statement5 of 9

f(p^a) = p for a prime p and a ≥ 2 (recorded by Erdős–Szekeres [ErSz78]). In particular, since (p^a) / P(p^a) = p^{a-1}, the prime power p^a is a "hit" (f(n) = n / P(n)) if and only if a = 2.

FormalConjectures/ErdosProblems/700.leanErdos700.erdos_700.variants.prime_pow1 lineExact file
∀ (p a : ℕ), Nat.Prime p → 2 ≤ a → Erdos700.f (p ^ a) = p
SolvedStatement only, no proof