{"schema":"vela.problem-packet.v0.1","problem":436,"statement":"If $p$ is a prime and $k,m\\geq 2$ then let $r(k,m,p)$ be the minimal $r$ such that $r,r+1,\\ldots,r+m-1$ are all $k$th power residues modulo $p$. Let\\[\\Lambda(k,m)=\\limsup_{p\\to \\infty} r(k,m,p).\\]Is it true that $\\Lambda(k,2)$ is finite for all $k$? Is $\\Lambda(k,3)$ finite for all odd $k$? How large are they?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A000445","name":"Latest possible occurrence of the first consecutive pair of n-th power residues, modulo any prime.","terms":"9,77,1224,7888,202124,1649375","url":"https://oeis.org/A000445"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}