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#!/usr/bin/env python
def findPandQ(a):
p = (
(a[2] * a[2] - a[1] * a[3])
/
(a[0] * a[2] - a[1] * a[1])
)
q = (
(a[0] * a[3] - a[2] * a[1])
/
(a[0] * a[2] - a[1] * a[1])
)
return(p, q)
def isLinearRecurranceOfSecondOrder(a):
(p1, q1) = findPandQ(a[0:4])
(p2, q2) = findPandQ(a[1:5])
if p1 != p2 or q1 != q2:
print(f'Values for P ({p1}, {p2}) ', end='')
print(f'and Q ({q1}, {q2}) ', end='')
print(f'are not consistent across all five elements')
return False
if p1 != int(p1) or q1 != int(q1):
print(f'Values for P ({p1}) ', end='')
print(f'and Q ({q1}) ', end='')
print(f'for first four elements are not integers')
return False
print(f'Found integer values for P ({int(p1)}) ', end='')
print(f'and Q ({int(q1)})')
return True
def comma_join(a):
return ', '.join(map(str, a))
def solution(a):
print(f'Input: @a = ({comma_join(a)})')
result = isLinearRecurranceOfSecondOrder(a)
print(f'Output: {result}')
print('Example 1:')
solution([1, 1, 2, 3, 5])
print('\nExample 2:')
solution([4, 2, 4, 5, 7])
print('\nExample 3:')
solution([4, 1, 2, -3, 8])
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