<正> Niederreiter and Robinson (J. Austral. Math. Soc. (Series A), 33 (1982), 197—212) proved that for a finite field F_q with odd q, any complete mapping polynomial of F_q has reduced degree ≤q-3 (q> 3). They indicated that it would
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be a pl.Oblem ofi一lterest to determi丁le whetherthe above result holds also for even q. We have solved the Problem with an affir功a-tivea赴swertheorem.1 .e.、ve ha祀Proved亡he fo21owi,29 T卜eore功.肠矛口二,比>3,a兀,。。mpZe才e彻,-九口脚l万呢o”;落aZ ofF;