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120 MATHEMATICA Acta Univ ACTA UNIVERSITATIS OULUENSIS Arch assumed beginning class number conditions given congruence modulo considered dealing degree Denote Department of Mathematics DIOPHANTINE EQUATION Cx2 discussed Editor examined equation Fermatschen Satz Finally finite number Finland following Theorem Gleichungen I(mod integen iolution Let q Ljunggren Math Mathematics University Nagell number of solutions obtain odd integers odd integers x odd iolutioni odd prime OLAVI KORHONEN Department paper positive integers possible present primes q Professor SAKARI PIHA proved regarding result SCIENTIAE RERUM NATURALIUM SERIES A SCIENTIAE solutions in integers solutions in odd solvability in integers solved Specially square-free squared factor Stolt takes the form theory Thue tine tion Uber University of Oulu upper valuable values wish to express