Erdős Problem #436
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
`IsPowerResidue k p a` means that \(a\) is a \(k\)th power residue modulo \(p\), that is, \(p \nmid a\) and \(a \equiv x^k \pmod{p}\) for some \(x\).
`r k m p` is the least \(r \geq 1\) such that \(r, r + 1, \ldots, r + m - 1\) are all \(k\)th power residues modulo \(p\), or `⊤` if there is no such \(r\).
\(\Lambda(k, m) = \limsup_{p \to \infty} r(k, m, p)\), where \(p\) runs over the primes.
Attempts
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The Mills-realizable coloring \(c(n)=\sum_{q\notin\{2,5,7\}}v_q(n)\bmod5\) has first zero triple \(37,329,226\), proving \(\Lambda(5,3)\ge37,329,226\) (and the same for odd \(5\mid k\)); finiteness re
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