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erdős #980

← #979 · #981 → (packet.json; erdosproblems.com)

Let $k \geq 2$ and $n_{k} (p)$ denote the least $k$ th power nonresidue of $p$ . Is it true that $p < x \sum n_{k} (p) \sim c_{k} \frac{x}{lo g x}$ for some constant $c_{k} > 0$ ?

Worked, still open.

number theory · solved · 0 attempts

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A053760 — Smallest positive quadratic nonresidue modulo p, where p is the n-th prime.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,A098990 — Decimal expansion of Sum_{n>=1} prime(n)/(2^n).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,

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Create a formalisation here · link

\sum \frac{p _{n}}{2 ^{n}}

irrational? (Here

p_{n}

n

th prime.)A098990

status

solved

finding.noted · reviewer:will-blair · 1 day

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