MathDB
13rd ibmo - rep. dominicana 1998/q6.

Source: Spanish Communities

April 16, 2006
floor functionmodular arithmeticalgebra solvedalgebra

Problem Statement

Let λ\lambda the positive root of the equation t2−1998t−1=0t^2-1998t-1=0. It is defined the sequence x0,x1,x2,…,xn,…x_0,x_1,x_2,\ldots,x_n,\ldots by x_0=1,\ x_{n+1}=\lfloor\lambda{x_n}\rfloor\mbox{ for }n=1,2\ldots Find the remainder of the division of x1998x_{1998} by 19981998. Note: ⌊x⌋\lfloor{x}\rfloor is the greatest integer less than or equal to xx.
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