Erdős problem 979 · problems.science

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

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Erdős [Er37b] proved that if $f_2(n)$ counts the number of solutions to $n = p_1^2 + p_2^2$ , where $p_1$ and $p_2$ are prime numbers, then $\limsup f_2(n) = \infty$ .

[Er37b] Erdős, Paul, On the Sum and Difference of Squares of Primes. J. London Math. Soc. (1937), 133--136.

FormalConjectures/ErdosProblems/979.leanErdos979.erdos_979.variants.k21 lineExact file

1Filter.limsup (fun n => (Erdos979.solutionSet n 2).encard) Filter.atTop = ⊤

SolvedStatement only, no proof

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