{"schema":"vela.problem-packet.v0.1","problem":980,"statement":"Let $k\\geq 2$ and $n_k(p)$ denote the least $k$th power nonresidue of $p$. Is it true that\\[\\sum_{p<x} n_k(p)\\sim c_k \\frac{x}{\\log x}\\]for some constant $c_k>0$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A053760","name":"Smallest positive quadratic nonresidue modulo p, where p is the n-th prime.","terms":"2,2,2,3,2,2,3,2,5,2,3,2,3,2,5,2,2,2,2,7,5,3,2,3,5,2,3,2,2,3,3,2,3,2,2,3,2,2,5,2,2,2,7,5,2,3,2,3,2,2,3,7,7,2,3,5,2,3,2,3,","url":"https://oeis.org/A053760"},{"id":"A098990","name":"Decimal expansion of Sum_{n>=1} prime(n)/(2^n).","terms":"3,6,7,4,6,4,3,9,6,6,0,1,1,3,2,8,7,7,8,9,9,5,6,7,6,3,0,9,0,8,4,0,2,9,4,1,1,6,7,7,7,9,7,5,8,8,7,7,9,4,3,7,3,2,8,3,1,2,2,0,","url":"https://oeis.org/A098990"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}