Erdős problem 979

Let $k ≥ 2$ , and let $f_k(n)$ count the number of solutions to $n = p_1^k + \dots + p_k^k$ , where the $p_i$ are prime numbers. Is it true that $\limsup f_k(n) = \infty$ ?

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FormalConjectures/ErdosProblems/

979.lean

Retained formal statement1 of 3

Let $k ≥ 2$ , and let $f_k(n)$ count the number of solutions to $n = p_1^k + \dots + p_k^k$ , where the $p_i$ are prime numbers. Is it true that $\limsup f_k(n) = \infty$ ?

FormalConjectures/ErdosProblems/979.leanErdos979.erdos_9791 lineExact file

1True ↔ ∀ k ≥ 2, Filter.limsup (fun n => (Erdos979.solutionSet n k).encard) Filter.atTop = ⊤

OpenStatement only, no proof