Added problem 66 to project_euler

[Kalyani123kumari]

Describe your change:

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
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• If this pull request resolves one or more open issues then the commit message contains Fixes: #{$ISSUE_NO}.

[dhruvmanila]

Suggested change

	Project Euler 66
	https://projecteuler.net/problem=66
	https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Algorithm
	Consider quadratic Diophantine equations of the form:
	x^2 – Dy^2 = 1
	For example, when D=13, the minimal
	solution in x is 6492 – 13×1802 = 1.
	It can be assumed that there are no solutions in
	positive integers when D is square.
	By finding minimal solutions in x for
	D = {2, 3, 5, 6, 7}, we obtain the following:
	3^2 – 2×2^2 = 1
	2^2 – 3×1^2 = 1
	9^2 – 5×4^2 = 1
	5^2 – 6×2^2 = 1
	8^2 – 7×3^2 = 1
	Hence, by considering minimal solutions in x for D ≤ 7,
	the largest x is obtained when D=5.
	Find the value of D ≤ 1000 in minimal solutions of
	x for which the largest value of x is obtained.
	Project Euler problem 66: https://projecteuler.net/problem=66
	Consider quadratic Diophantine equations of the form:
	x^2 – Dy^2 = 1
	For example, when D=13, the minimal
	solution in x is 6492 – 13×1802 = 1.
	It can be assumed that there are no solutions in
	positive integers when D is square.
	By finding minimal solutions in x for
	D = {2, 3, 5, 6, 7}, we obtain the following:
	3^2 – 2×2^2 = 1
	2^2 – 3×1^2 = 1
	9^2 – 5×4^2 = 1
	5^2 – 6×2^2 = 1
	8^2 – 7×3^2 = 1
	Hence, by considering minimal solutions in x for D ≤ 7,
	the largest x is obtained when D=5.
	Find the value of D ≤ 1000 in minimal solutions of
	x for which the largest value of x is obtained.
	References:
	- https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Algorithm

[dhruvmanila]

A better description of what the function does.

[dhruvmanila]

Descriptive variable names, please.

[dhruvmanila]

This seems unnecessary. Please remove it.

[dhruvmanila]

Descriptive function and parameter name.
Proper type hints needed: https://docs.python.org/3/library/typing.html

[dhruvmanila]

Suggested change

	"""
	function to find value of D in minimal solutions of x
	for which x is largest.
	"""
	"""
	>>> solution(7)
	5
	"""
	"""
	function to find value of D in minimal solutions of x
	for which x is largest.
	>>> solution(7)
	5
	"""

A better description of what the function does.
Need more doctest

[dhruvmanila]

Descriptive variable names

[dhruvmanila]

This seems unnecessary. Please remove it.

[dhruvmanila]

This is not needed.

[dhruvmanila]

Suggested change

	print(f"{solution()}")
	print(f"{solution() = }")

[stale]

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