bibkey: zejnulahiarslanagic2001problem2623
authors: Faruk Zejnulahi; Sefket Arslanagic
year: 2001
title: "Problem 2623"
doi: null
url: https://cms.math.ca/wp-content/uploads/crux-pdfs/CRUXv27n2.pdf
claim: "For positive cyclic variables, define S_k as the sum over j=1 through n of the quotient of the consecutive block sum x_j through x_(j+k) by the shifted block sum x_(j+1) through x_(j+k+1). Prove or disprove that S_k >= S_(k+1)."
strata_touched:
  - D5/S0/Certificates/CruxProblem2623Refutation
license: citation-only
triage: anchor

Crux Problem 2623

Zejnulahi and Arslanagic ask whether the cyclic ratio sums satisfy S_k >= S_(k+1) for positive variables. The source PDF displays the problem on page 139; later Crux references cite it as [2001:138].

Verified locator

• URL: https://cms.math.ca/wp-content/uploads/crux-pdfs/CRUXv27n2.pdf
• Displayed page 139: Problem 2623 and the sentence “Prove or disprove that S_k >= S_(k+1).”

The source PDF has SHA-256 c2ce15e455786b1bac7e8ce360ebe4e106970b1efb0e290df6758821823a8e70. Crux volume 28, number 4, printed page 252 states that no solutions had been received and that the problem remained open; that PDF has SHA-256 efc023a15d6b5f0da497683ea0a9bc5809179cb27a933276616d40583e37adf9. The cumulative unsolved table in volume 36, number 8, printed page 547 lists 2623 [2001:138; 2002:252]; that PDF has SHA-256 5915536dfa6ba971fb37f3fe6a3361bcfba300dc817bc17c65d1c29a6b999c6b.

Whether a solution or refutation was published after the 2010 cumulative table is ASSUMED-UNVERIFIED. The searched scope did not establish exhaustive absence after 2010.