
def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					assert isinstance(lowerCAmelCase__				,    lowerCAmelCase__	), f'The input value of [n={number}] is not an integer'

					if number == 1:
										return 2
					elif number < 1:
										lowercase					=		f'The input value of [n={number}] has to be > 0'
										raise ValueError(lowerCAmelCase__	)
					else:
										lowercase					=		sylvester(number - 1	)
										lowercase					=		num - 1
										lowercase					=		num
										return lower * upper + 1


if __name__ == "__main__":
							print(F'The 8th number in Sylvester\'s sequence: {sylvester(8)}')






def  UpperCamelCase					(							lowerCAmelCase__ = 1000	):
					'''simple docstring'''
					lowercase					=		-1
					lowercase					=		0
					for a in range(1				,    n // 3	):
										# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
										lowercase					=		(n * n - 2 * a * n) // (2 * n - 2 * a)
										lowercase					=		n - a - b
										if c * c == (a * a + b * b):
															lowercase					=		a * b * c
															if candidate >= product:
																				lowercase					=		candidate
					return product


if __name__ == "__main__":
							print(F'{solution() = }')




