A sequence defined by a rule from earlier terms is a recurrence. The Fibonacci numbers are the classic: each is the sum of the previous two. Many recurrences have a closed form, for Fibonacci it involves the golden ratio, but computing them term by term is often the clearest path.
tusaale · fib(20)
tallaabo tallaabo
- F_0 = 0,; F_1 = 1
Each Fibonacci number is the sum of the two before it.
- F_{2} = F_{1} + F_{0} = 1
- F_{3} = F_{2} + F_{1} = 2
- F_{4} = F_{3} + F_{2} = 3
- F_{5} = F_{4} + F_{3} = 5
- F_{6} = F_{5} + F_{4} = 8
- F_{7} = F_{6} + F_{5} = 13
- F_{8} = F_{7} + F_{6} = 21
- \vdots
- F_{19} = F_{18} + F_{17} = 4181
- F_{20} = F_{19} + F_{18} = 6765
Jawaabta muuji
Haddaad Dooro dhibaato, ama qoraal ama sawirkaaga. Talaab kasta, sawir, jawaabta qarsoon ilaa aad weydiiso.
A xisaab bilaash ah oo ku daray qoraalada waxbarasho kasta, diiwaanka waxa aad dhamaatay, dhibaatooyinka aad xal u tahay meel kaliya, iyo macallinka aad weydiisan kartaa oo ku saabsan bogga. Xisaabta oo keliya waa u furan yahay qof kasta, la diiwaan geliyey ama aan.
Ku soo biir Ku soo galCalaamadaha la isticmaalay halkan
Taab calaamad kasta oo loogu talagalay qeexidda buuxda, sawir, iyo waxa xarfaha oo dhan ka mid ah ka dhigan tahay.
Sida loo: Sequences
- Each Fibonacci number is the sum of the two before it.
Su'aalaha dadku waydiiyaan
Why are primes so important?
Every integer factors into primes in exactly one way, so primes are the atoms of multiplication. Cryptography relies on that factoring being easy to state and hard to do.
How do I tell whether a big number is prime?
Trial division up to the square root works for small numbers. For large ones, probabilistic tests (Miller-Rabin) give an answer that is wrong with negligible probability, and deterministic tests (AKS) exist but are slower.
In ka badan Number Theory
Prime factorisationPrime numbersGCD and LCMModular arithmeticDivisorsNumber basesDiophantine equationsFermat's little theorem and Euler's theoremRSA: cryptography from number theory