Period of the Fibonacci sequence modulo an integer
Plot of the first 10,000 Pisano periods.
In number theory, the nth Pisano period, written as π(n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of periodic functions in Fibonacci numbers was noted by Joseph Louis Lagrange in 1774.[1][2]
^Weisstein, Eric W. "Pisano Period". MathWorld.
^On Arithmetical functions related to the Fibonacci numbers. Acta Arithmetica XVI (1969). Retrieved 22 September 2011.
theory, the nth Pisanoperiod, written as π(n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named...
Pisano (surname), a list of people Pisano, Piedmont, commune in the province of Novara, in northern Italy Pisanoperiod, in number theory Pisanello (1380–1456)...
Brahmagupta–Fibonacci identity, the Fibonacci search technique, and the Pisanoperiod. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765...
Nicola Pisano (also called Niccolò Pisano, Nicola de Apulia or Nicola Pisanus; c. 1220/1225 – c. 1284) was an Italian sculptor whose work is noted for...
with period at most 6n. The lengths of the periods for various n form the so-called Pisano periods. Determining a general formula for the Pisano periods...
exponentiation Modulo (mathematics) Multiplicative group of integers modulo n Pisanoperiod (Fibonacci sequences modulo n) Primitive root modulo n Quadratic reciprocity...
the Unnatural") Fibonacci sequence and modular arithmetic (see also Pisanoperiod) ("The Case of the Willing Parrot") Kinematics ("The Problem of the...
Duomo: exhibiting among others the original sculptures of Nicola Pisano and Giovanni Pisano, the Islamic Pisa Griffin, and the treasures of the cathedral...
a(p) is defined for every prime p. The rank of apparition divides the Pisanoperiod π(p) and allows to determine all Fibonacci numbers divisible by p. For...
4% DiFiore (L) with 2%; Pisano (C) with 1%; Undecided with 8% DiFiore (L) and Pisano (C) with 1%; Undecided with 12% Pisano (C) with 2%; DiFiore (L)...
artistic return to classicism had been exemplified in the sculpture of Nicola Pisano, Florentine painters led by Masaccio strove to portray the human form realistically...
1450/1455), born Antonio di Puccio Pisano or Antonio di Puccio da Cereto, also erroneously called Vittore Pisano by Giorgio Vasari, was one of the most...
suffers from schizophrenia, is partly based on Holcomb. Smith, Michael A.; Pisano, Louis R. (2018). Jaws 2: The Making of the Hollywood Sequel (Updated and...
Sometime during the period 1512 to 1520, he was the teacher of Francesco Corteccia, organist and composer to Cosimo I de' Medici. Pisano remained based in...
design had long been attributed to a man named Guglielmo and to Bonanno Pisano, the latter a well-known 12th-century resident artist of Pisa known for...
an autonomous, self-consistent work of art" (John Pope-Hennessy). Nicola Pisano (1258–78) and his son Giovanni developed a style that is often called Proto-Renaissance...
Bonanno Pisano (original bronze doors) Giambologna and his school (bronze doors of the facade) Giovanni Pisano (pulpit) Nicola Pisano e Giovanni Pisano (crown...
period that inherited this new way of making sculpture in the figure of Nicola Pisano, followed by his son Giovanni Pisano, and later Andrea Pisano (first...
sculptor of the period was Arnolfo di Cambio (c. 1240 – 1300/1310), who was also an architect. Born in Tuscany, he also trained with Nicola Pisano, and was his...
his brother Pietro. Important sculptors included two pupils of Giovanni Pisano: Arnolfo di Cambio and Tino di Camaino, and Bonino da Campione. The Trecento...
The Pisan calendar, also referred to as the stile pisano ("Pisan style") or the calculus Pisanus ("Pisan calculation"), was the calendar used in the Republic...
late 13th and early 14th centuries, the sculpture of Nicola Pisano and his son Giovanni Pisano, working at Pisa, Siena and Pistoia shows markedly classicising...
was overseen by Giovanni Pisano whose work on the Duomo's façade and the pulpit was influenced by his father Nicola Pisano. The lower portion of the...
Grand Duchy of Tuscany Duchy of Savoy Renaissance Italian Wars Early Modern period Napoleonic Italy Austrian occupation and Kingdom of Lombardy-Venetia Kingdom...
Retrieved 28 August 2023.; See the books from Italian historian Giorgio Pisanò Storia della guerra civile in Italia, 1943–1945, 3 voll., Milano, FPE, 1965...
1990, Jimmy Pisano opened a new bar at 53 Christopher Street, which was initially named New Jimmy's before becoming Stonewall. After Pisano's death in 1994...
original on 19 April 2014. Retrieved 28 March 2012. Pisano (1977), p. 124 Pisano (1977), p. 128 Pisano (1977), p. 125 Menichetti, M.; Lodolo, E.; Tassone...
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