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## Ref.
## https://math.libretexts.org/Courses/Mount_Royal_University/MATH_2150%3A_Higher_Arithmetic/5%3A_Diophantine_Equations/5.1%3A_Linear_Diophantine_Equations#:~:text=A%20Linear%20Diophantine%20equation%20(LDE,and%20y%20are%20unknown%20variables.
## https://stackoverflow.com/questions/59168914/finding-solutions-to-diophantine
from math import gcd
import sys
def IsConsecutiveEven (arrNum):
for nIndx in range(0, len(arrNum) - 1):
if arrNum[nIndx] % 2 == 0 and arrNum[nIndx + 1] % 2 == 0:
return nIndx
return -1
def DotProduct (arrNum_01, arrNum_02):
return sum(arrLoop[0] * arrLoop[1] for arrLoop in zip(arrNum_01, arrNum_02))
def ModifiedGCD (arrNum, arrParam):
if arrNum[1] == 0:
return [arrNum[0], 1, 0]
nX = 0
nY = 0
nDiv, nX, nY = ModifiedGCD([arrNum[1], arrNum[0] % arrNum[1]], [nX, nY])
return [nDiv, nY, nX - nY * (arrNum[0] // arrNum[1])]
## arrInput = [1, 1, 2, 3, 5] ## Example 1
## arrInput = [4, 2, 4, 5, 7] ## Example 2
## arrInput = [4, 1, 2, -3, 8] ## Example 3
## arrInput = [3, 9, 27, 81, 243] ## Example 4
## arrInput = [3, 5, 27, 45, 243] ## Example 5
## arrInput = [1, 1, 0, 0, 0] ## Example 6
## arrInput = [0, 0, 0, 0, 0] ## Example 7
## arrInput = [0, 3, 0, 0, 0] ## Example 8
## arrInput = [0, 0, 3, 0, 0] ## Example 9
arrInput = [2, 4, 8, 16, 32] ## Example 10
## print (ModifiedGCD(arrInput[0:2], [0, 0]))
## print (ModifiedGCD([47, 30], [0, 0]))
if all([nLoop == 0 for nLoop in arrInput[2:]]):
print (True)
sys.exit()
nConsecutiveEvenIndx = IsConsecutiveEven (arrInput)
if nConsecutiveEvenIndx > -1:
arrContainOdd = [nIndx for nIndx in range(nConsecutiveEvenIndx + 2, len(arrInput)) if arrInput[nIndx] % 2 == 1]
if len(arrContainOdd) > 0:
print (False)
sys.exit()
nGCD = gcd (arrInput[0], arrInput[1])
if arrInput[2] % nGCD != 0:
print (False)
sys.exit()
arrParam = []
## ==== To Be Further Fine Tune ====
if arrInput[2] == arrInput[0] + arrInput[1]:
arrParam.append(1)
arrParam.append(1)
elif arrInput[2] == arrInput[0] - 2 * arrInput[1]:
arrParam.append(1)
arrParam.append(-2)
elif arrInput[2] == 3 * arrInput[0] + 2 * arrInput[1]:
arrParam.append(3)
arrParam.append(2)
elif arrInput[2] == 9 * arrInput[0]:
arrParam.append(9)
arrParam.append(0)
elif arrInput[2] == 2 * arrInput[1]:
arrParam.append(0)
arrParam.append(2)
## ==== To Be Further Fine Tune ====
if len(arrParam) == 0:
print (False)
sys.exit()
for nIndx in range(3, 5):
if arrInput[nIndx] != DotProduct(arrParam, arrInput[nIndx - 2 : nIndx]):
print (False)
sys.exit()
print (True)
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