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排列中相邻两项的最大公因子

, PP. 18-22

Keywords: 整数排列,最大公因子,下极限

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Abstract:

1983年,erd?sp,freudr和hegyvárin证明了对所有正整数的任一排列a1,a2,a3,…,有liminfi(ai,ai+1)/i≤61/90.本文将结果改进为liminfi(ai,ai+1)/i≤13/20.

References

[1]  ??freudr.onsumsofsubsequenttermsofpermutations[j].actamathhungar,1983,41(1/2):177??185.
[2]  ??dvornicichr.onaproblemofcyclicpermutationsofintegers[j].discreteapplmath,1980,2(4):353??355.
[3]  ??sidorenkoaf.aninfinitepermutationwithoutarithmeticprogressions[j].discretemath,1988,69(2):211.
[4]  ??polyakovab.onequilibriumdistributionsonthesetofpermutationsofintegers[j].russianmathsurveys,1999,54(2):450??452.
[5]  ??erd??sp,freudr,hegyv??rin.arithmeticalpropertiesofpermutationsofintegers[j].actamathhungar,1983,41(1/2):169??176.
[6]  ??saiase.applicationsdesentiers??diviseursdenses[j].actaarith,1998,83(3):225??240.

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