The site's wording defines $n_k(p)$ as the least $k$th power nonresidue of $p$ for every prime $p$, as Erdős's texts do ((79) of [Er65b], the site's source, printed p. 232; conjecture (4) of [Er61e], p. 11), and leaves it undefined at the primes with $\gcd(k,p-1)=1$, which have no $k$th power nonresidue. Read as a sum over the primes that have one, it includes, for composite $k$, the primes $p\not\equiv1\pmod k$ with $d=\gcd(k,p-1)>1$, whose least $k$th power nonresidue is $n_d(p)$; for prime $k$ only the primes $p\equiv1\pmod k$ contribute. Elliott [El67b] defines $n_k(p)$ in the paper's introduction for $p\equiv1\pmod k$ and sets $n_k(p)=0$ for every other prime, and the paper's Theorem 1 proves the asymptotic under that convention for every $k\ge2$ (indeed with any exponent $a<4e^{1-1/k}$ in place of $1$, and with the explicit constant $\sum_r k^{-r}q_r$ over the primes $q_r$ when $k$ is an odd prime). The site labels the problem PROVED and its commentary says "The general case was proved by Elliott [El67b]", without remarking on the convention. The curator therefore reads the sum as Elliott does, and the precise Statement adopts Elliott's convention. The change inserts Elliott's definition of $n_k(p)$; nothing else changes. For prime $k$ the two readings agree, since a prime $p\not\equiv1\pmod k$ then has every residue a $k$th power. For composite $k$ they differ: under the precise Statement the problem is proved for every $k\ge2$ by Elliott's Theorem 1 (claim page (Elliott, 1967)); under the site's wording the contribution of the primes $p\not\equiv1\pmod k$ with $\gcd(k,p-1)>1$ is covered by no recorded source, so that reading is open for composite $k$ and is recorded as a variant under Formulation. Erdős [Er61e] proved the case $k=2$, where the readings agree, with $c_2=\sum_j p_j/2^j$ (claim page (Erdős, 1961)). The curator's reading is inferred from the label and the credit alone; no text of the curator's states the convention.