YouTube and arXiv Dominate Search; IMO 1988 Problem 6 Emerges as Sole Concrete Math Artifact — E8 Intelligence Research

{"FINDING:":[0],"The":[1,28,125,163],"search":[2,161],"results":[3],"are":[4],"dominated":[5],"by":[6],"YouTube":[7],"videos":[8],"and":[9,51,134],"one":[10],"arXiv":[11,53,164],"proceedings":[12],"volume;":[13],"no":[14,149],"specific":[15],"unsolved":[16],"problem":[17],"or":[18,120,154],"novel":[19],"mathematical":[20,31,56],"discovery":[21],"is":[22,33,46,77,87,103,143,157],"extracted":[23],"from":[24],"the":[25,34,52,94,160,175],"content":[26],"itself.":[27],"only":[29],"concrete":[30],"artifact":[32],"reference":[35],"to":[36],"IMO":[37,62,126],"1988":[38,63,127],"Problem":[39],"6":[40],"(the":[41],"famous":[42],"\\"a²+b²":[43],"/":[44],"(ab+1)":[45],"a":[47,78,88,110,131,139,144],"perfect":[48,79],"square\\"":[49],"problem),":[50],"volume":[54],"on":[55,138],"physics":[57],"olympiad":[58],"problems.":[59],"|":[60,123],"MATH:":[61],"P6:":[64],"Let":[65],"a,b":[66],"be":[67],"positive":[68],"integers":[69],"such":[70],"that":[71],"ab+1":[72],"divides":[73],"a²+b².":[74],"Then":[75],"(a²+b²)/(ab+1)":[76],"square.":[80],"Proof":[81],"uses":[82],"Vieta":[83],"jumping:":[84],"if":[85],"(a,b)":[86],"solution":[89,112,129],"with":[90],"minimal":[91],"a+b,":[92],"then":[93],"other":[95],"root":[96],"of":[97,174],"x²":[98],"-":[99,107],"k·b·x":[100],"+":[101],"(b²-k)=0":[102],"a'":[104],"=":[105],"k·b":[106],"a,":[108],"yielding":[109],"smaller":[111],"unless":[113],"a'=0,":[114],"forcing":[115],"k=b².":[116],"No":[117],"new":[118],"constants":[119],"ratios":[121],"appear.":[122],"CONNECTION:":[124],"P6":[128],"involves":[130],"quadratic":[132],"form":[133],"integer":[135],"lattice":[136],"points":[137],"hyperbola":[140],"—":[141],"this":[142],"Diophantine":[145],"geometry":[146],"structure,":[147],"but":[148],"explicit":[150],"golden":[151],"ratio,":[152],"base-60,":[153],"crystallographic":[155],"symmetry":[156],"present":[158],"in":[159],"results.":[162],"vo":[165],"Author:":[166],"Andrew":[167],"Stewart":[168],"Caldin,":[169],"Independent":[170],"Researcher,":[171],"UK.":[172],"Part":[173],"E8":[176],"Intelligence":[177],"Research":[178],"series.":[179],"Platform:":[180],"e8intelligence.com":[181]}

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-17
DOI
https://doi.org/10.5281/zenodo.22805638
Primary Topic
Benford’s Law and Fraud Detection
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
preprint

YouTube and arXiv Dominate Search; IMO 1988 Problem 6 Emerges as Sole Concrete Math Artifact — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
preprint

YouTube and arXiv Dominate Search; IMO 1988 Problem 6 Emerges as Sole Concrete Math Artifact — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: The search results are dominated by YouTube videos and one arXiv proceedings volume; no specific unsolved problem or novel mathematical discovery is extracted from the content itself. The only concrete mathematical artifact is the reference to IMO 1988 Problem 6 (the famous "a²+b² / (ab+1) is a perfect square" problem), and the arXiv volume on mathematical physics olympiad problems. | MATH: IMO 1988 P6: Let a,b be positive integers such that ab+1 divides a²+b². Then (a²+b²)/(ab+1) is a perfect square. Proof uses Vieta jumping: if (a,b) is a solution with minimal a+b, then the other root of x² - k·b·x + (b²-k)=0 is a' = k·b - a, yielding a smaller solution unless a'=0, forcing k=b². No new constants or ratios appear. | CONNECTION: The IMO 1988 P6 solution involves a quadratic form and integer lattice points on a hyperbola — this is a Diophantine geometry structure, but no explicit golden ratio, base-60, or crystallographic symmetry is present in the search results. The arXiv vo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

YouTube and arXiv Dominate Search; IMO 1988 Problem 6 Emerges as Sole Concrete Math Artifact — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS