Fibonacci numbers and Fermat's last theorem
TLDR
In this article, it was shown that the affirmative answer to Wall's question implies the first case of FLT (Fermat's last theorem) for exponents which are (odd) Fibonacci primes or Lucas primes.Abstract:
numbers. As applications we obtain a new formula for the Fibonacci quotient Fp−( 5 p )/p and a criterion for the relation p |F(p−1)/4 (if p ≡ 1 (mod 4)), where p 6= 5 is an odd prime. We also prove that the affirmative answer to Wall’s question implies the first case of FLT (Fermat’s last theorem); from this it follows that the first case of FLT holds for those exponents which are (odd) Fibonacci primes or Lucas primes.read more
Citations
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Journal ArticleDOI
A search for Wieferich and Wilson primes
TL;DR: It is reported that there exist no new Wieferich primes p < 4 x 10 12 , and no new Wilson prime p < 5x 10 8 .
Journal ArticleDOI
An Introduction to the Theory of Numbers. By I. Niven and H. S. Zuckerman. Pp. 250. 50s. 1960. (Wiley, London and New York)
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The multidimensional maximum entropy moment problem: a review of numerical methods
TL;DR: In this article, a numerical method for the multidimensional moment-constrained maximum entropy problem was developed, which is practically capable of solving maximum entropy problems in the two-dimensional domain and in the threedimensional domain.
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New congruences for central binomial coefficients
Zhi-Wei Sun,Roberto Tauraso +1 more
TL;DR: In this paper, it was shown that if p 2,5, [email protected]?k=1p-1(2kk)k=89p^2B"p"-"3(modp^3), where B"n denotes the nth Bernoulli number.
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Binomial coefficients, Catalan numbers and Lucas quotients
TL;DR: In this paper, it was shown that for any integer n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 28
References
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Book
History of the Theory of Numbers
Abstract: THE third and concluding volume of Prof. Dickson's great work deals first with the arithmetical. theory of binary quadratic forms. A long chapter on the class-number is contributed by Mr. G. H. Cresse. Next comes an account of existing knowledge on quadratic forms in three or more variables, followed by chapters on cubic forms, Hermitian and bilinear forms, and modular invariants and covariants.History of the Theory of Numbers.Prof. Leonard Eugene Dickson. Vol. 3: Quadratic and Higher Forms. With a Chapter on the Class Number by G. H. Cresse. (Publication No. 256.) Pp. v + 313. (Washington: Carnegie Institution, 1923.) 3.25 dollars.
Journal ArticleDOI
Fibonacci Series Modulo m
TL;DR: In this paper, the Fibonacci Series Modulo m is modulo m. The American Mathematical Monthly: Vol. 67, No. 6, pp. 525-532.
Book
13 lectures on Fermat's last theorem
TL;DR: In this article, Kummer's Monumental Theorem was used to prove that Fermat's Last Theorem is true for every prime exponent less than 125,000, and the first case is True for infinitely many pairwise Relatively Prime Exponents.