✦ 5 frontiers

read-only vieweressays

erdős #220

← #219 · #221 → (packet.json; erdosproblems.com)

Let $n \geq 1$ and $A = {a_{1} < \dots < a_{ϕ (n)}} = {1 \leq m < n : (m, n) = 1} .$ Is it true that $1 \leq k < ϕ (n) \sum (a_{k + 1} - a_{k})^{2} ≪ \frac{n ^{2}}{ϕ ( n )} ?$

Worked, still open.

number theory · solved · prize $500 · 0 attempts

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

oeis

A322144 — a(n) = Sum_{i=1..phi(n)-1} (r(i+1)-r(i))^2 where r(1) = 1 < ... < n-1 = r(phi(n)) are the phi(n) integers relatively prime to n.0,0,1,4,3,16,5,12,11,24,9,36,11,32,29,28,15,56,17,52,39,48,21,76,31,56,41,68,27,128,29,60,59,72,57,116,35,80,69,108,39,1

links

Create a formalisation here · link

status

solved

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

renders the record as of vev_d199cb2e · 1,338 events · hub