New Types of Congruences Involving Bernoulli Numbers and Fermat's Quotient.
نویسنده
چکیده
make Mp prime are 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257. Comparison of this list with the correct data recorded in the top line of the table presented below shows that Mersenne made five mistakes. p = 67 and 257 do not yield prime values for Mp, and p = 61, 89 and 107 were not included in his list of special primes. With reference to explicit factoring, attention should be called to a valuable paper4 by Professor D. H. Lehmer entitled "On the Factors of 2n 1." His investigations on 76 numbers unveiled eleven factors which fall within Mersenne's range. Incidentally two of his new factors confirmed the present writer's final residues for M167 and M229.
منابع مشابه
Statement Julian
My mathematical research interests are in number theory and algebraic geometry. My thesis work concerns the arithmetic of a family of rational numbers known as multiple harmonic sums, which are truncated approximations of multiple zeta values. I explore new structures underlying relations involving multiple harmonic sums, p-adic L-values, Bernoulli numbers, and binomial coefficients. This is us...
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عنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 34 3 شماره
صفحات -
تاریخ انتشار 1948