The Weekly Challenge

10. TASK #2: Linear Recurrence of Second Order

HEADLINES

Welcome to the Week #246 of The Weekly Challenge.

Today is the first monday of the month and time to declare next champion. With great pleasure, I would like to announce, Peter Meszaros as the next champion of the weekly challenge. As of today, he has contributed 50 Perl solutions to the weekly challenge.

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RECAP

Quick recap of The Weekly Challenge - 245 by Mohammad S Anwar.

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Task 1: 6 out of 49

Submitted by: Andreas Voegele

6 out of 49 is a German lottery.

Write a script that outputs six unique random integers from the range 1 to 49.

Output

Task 2: Linear Recurrence of Second Order

Submitted by: Jorg Sommrey

You are given an array @a of five integers.

Write a script to decide whether the given integers form a linear recurrence of second order with integer factors.

A linear recurrence of second order has the form

a[n] = p * a[n-2] + q * a[n-1] with n > 1

where p and q must be integers.

Example 1

Input: @a = (1, 1, 2, 3, 5)
Output: true

@a is the initial part of the Fibonacci sequence a[n] = a[n-2] + a[n-1]
with a[0] = 1 and a[1] = 1.

Example 2

Input: @a = (4, 2, 4, 5, 7)
Output: false

a[1] and a[2] are even. Any linear combination of two even numbers with integer factors is even, too.
Because a[3] is odd, the given numbers cannot form a linear recurrence of second order with integer factors.

Example 3

Input: @a = (4, 1, 2, -3, 8)
Output: true

a[n] = a[n-2] - 2 * a[n-1]

Last date to submit the solution 23:59 (UK Time) Sunday 10th December 2023.