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In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
In mathematics, the Skolem problem is the problem of determining whether the values of a constant-recursive sequence include the number zero. The problem can be formulated for recurrences over different types of numbers, including integers, rational numbers, and algebraic numbers.
A linear recurrence denotes the evolution of some variable over time, with the current time period or discrete moment in time denoted as t, one period earlier denoted as t − 1, one period later as t + 1, etc. The solution of such an equation is a function of t, and not of any iterate values, giving the value of the iterate at any time.
The order of the sequence is the smallest positive integer such that the sequence satisfies a recurrence of order d, or = for the everywhere-zero sequence. [ citation needed ] The definition above allows eventually- periodic sequences such as 1 , 0 , 0 , 0 , … {\displaystyle 1,0,0,0,\ldots } and 0 , 1 , 0 , 0 , … {\displaystyle 0,1,0,0 ...
LUC is a public-key cryptosystem based on Lucas sequences [5] that implements the analogs of ElGamal (LUCELG), Diffie–Hellman (LUCDIF), and RSA (LUCRSA). The encryption of the message in LUC is computed as a term of certain Lucas sequence, instead of using modular exponentiation as in RSA or Diffie–Hellman.
In the spiral, each triangle shares a side with two others giving a visual proof that the Padovan sequence also satisfies the recurrence relation = + ()Starting from this, the defining recurrence and other recurrences as they are discovered, one can create an infinite number of further recurrences by repeatedly replacing () by () + ()
In mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence relation, described below. They were discovered by mathematician Michael Somos . From the form of their defining recurrence (which involves division), one would expect the terms of the sequence to be fractions, but surprisingly, a few Somos sequences have ...
The master theorem always yields asymptotically tight bounds to recurrences from divide and conquer algorithms that partition an input into smaller subproblems of equal sizes, solve the subproblems recursively, and then combine the subproblem solutions to give a solution to the original problem.