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Tag Archives: Fibonacci number
Fibonacci in arithmetic progression
Fibonacci numbers is defined by the recurrence relation: then, giving us all increasing arithmetic progressions formed of three terms of the Fibonacci sequence For example, Prove that there are no increasing arithmetic progressions formed of … Continue reading
Fibonacci numbers  Is F(m*n 1) – (F(n1))^m always divisible by (F(n))^2 ?
Is always divisible by for all and any counterexample?
Fibonacci numbers  gcd …. (Part 2)
The gcd of any two Fibonacci numbers is also a Fibonacci number > for all > > if divides , then divides If … Continue reading
The square of a Fibonacci number
Show that is the square of a Fibonacci number
Fibonacci numbers  is 5 F^2_{2k} + 4 always a square number?
Is always a square number? Also, is always a square number?
Fibonacci numbers  F(n) < x < F(n+1) < y < F(n+2)
If then show that is never a Fibonacci number
Fibonacci numbers  (F(n) F(n+3))^2 + (2 F(n+1) F(n+2))^2
Is a square number for all positive integers ?
Fibonacci num3ers : a surprising occurrence
To find positive integers such that are all squares that is, Note that It happens that the first few Fibonacci numbers can be used to … Continue reading
Sequence (A, B, C, D), (D – A) is a Fibonacci number
Fibonacci numbers are the numbers in the following integer sequence : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, … Continue reading
Fibonacci number  ceiling(√e^n) for n=0,1,…,8
The first few Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, … Continue reading