Perfect Numbers and Fibonacci Sequences

图书简介

In this book we first review the history and the current situation of the perfect number problem, including the origin of Mersenne prime number, and then the history and the current situation of Fibonacci sequence, both of which have our own research work. Later, we define the square perfect number, explore and reveal for the first time the secret relationship between square perfect number and Fibonacci sequence, Lucas sequence, twin prime conjecture and Fermat prime.Key FeaturesThe competitive advantage is described as above, moreover, as Albert Einstein said after he discovered the theory of relativity, "the real law is nonlinear"The discovery of square perfect number and its necessary and sufficient condition confirms this

Preface; The History of Perfect Numbers: What is Perfect Number?; Euclid’s Element; Nicomachus; Sum of Squares and Sum of Cubes; Haytham in Arabia; Mersenne Number and Mersenne Prime; Descartes and Fermat; Euler-Euclidean Theorem; Father Pervushin; Double L Prime Detection Method; GIMPS Project; Perfect Number Problem: Properties of Perfect Number; Perfect Number Problem; Odd Perfect Number; Touchard Theorem; Deficient Number and Abundant Number; Weird Number and Semi-Perfect Number; Ore Number and Harmonic Number; A Variety of Ore Numbers; Amicable Number; K-Perfect Number; Super Perfect Number; S-Perfect Number; Golden Ratio Conjecture; Fibonacci Sequence: Leonardo de Pisa; Rabbit Problem; General Term and Limit; Continued Fraction and Bound of Fn; Cassini Identity; The Equality of Binomial Coefficients; Divisible Sequences; Zeckendorf Theorem; From Binary to Ternary; 10TH Hilbert Problem; Lucas Number and Lucas Sequence: Lucas Number; Determination of Fibonacci Number; Prime Factor of Fibonacci Number; Congruences of Fibonacci Number; A Generalized Congruence; Properties of Narayana Sequences; Pythagoras Array; Diophantine Array; Generating Function; Lucas Sequence; Pisano Cycle; π(n) and π’(n); Prime Factor of Lucas Number; Perfect Number and Fibonacci Sequence: Square Perfect Number; Several Lemmas; Proof of the Theorems; A Conjecture of Perfect Number; Square Perfect Number with Constant Term; Square Perfect Number and Twin Prime Conjecture; Fermat Primes and GM Numbers; ABCD Equation; Application of Elliptic Curve; Lucas Sequence; Appendices: The First 100 Fibonacci Numbers and Lucas Numbers; Prime Factorization of the First 100 Fibonacci Numbers; Prime Factorization of the First 100 Lucas Numbers; References

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Perfect Numbers and Fibonacci Sequences 完全数与斐波那契序列 数论

Perfect Numbers and Fibonacci Sequences

完全数与斐波那契序列
数论