A problem of Erdős on abelian groups

Abstract

The following theorem is proved. Ifa 1,a 2, ...a n are nonzero elements inZ n , and are not all equal, then ε1 a 12 a 2+...+ε n a n =0 has at leastn solutions with ε i =0 or 1.

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References

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    R. B. Eggleton andP. Erdős, Two combinatorial problems in group theory,Acta Arith.21 (1972), 111–116.

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    J. E. Olson, A combinatorial problem on finite Abelian groups, II,J. Number Theory 1 (1969), 195–199.

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Olson, J.E. A problem of Erdős on abelian groups. Combinatorica 7, 285–289 (1987). https://doi.org/10.1007/BF02579305

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AMS subject classification (1980)

  • 20 K 01
  • 10 B 05