Fermat's Last Theorem and T H E Second Factor in T H E Cyclotomic Class Number
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چکیده
where / is an odd prime and x, y, z are rational integers prime to each other and none zero, we shall refer to the case where xyz is prime to / as case I ; if xyz = 0 (mod I) then we call this case II . I now give a sketch of a proof of a theorem which appears to be the principal result I have so far found concerning the first case of the last theorem. THEOREM 1. If (1) is possible in case I, then the second factor of the class number of the cyclotomic field defined by
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IH. S. Vandiver, "Fermat's Last Theorem," Am. Math. Mlonthly, 53, 567-568, 1946. 2 H. S. Vandiver, "The Relation of Some Data Obtained from Rapid Computing Machines to the Theory of Cyclotomic Fields, these PROCEEDINGS, 40, 474-480, 1954. 3H. S. Vandiver, "A Theorem of Kummer's concerning the Second Factor of the Class Number of a Cyclotomic Field," Bull. Am. Math. Soc., 35, 333-335, 1929. 4D. ...
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