Consider quadratic Diophantine equations of the form x2 - Dy2 = 1.
For example, when D = 13, the minimal solution in x is 6492 - 13 x 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:
32 - 2x22 = 1, 22 - 3x12 = 1, 92 - 5x42 = 1, 52 - 6x22 = 1, 82 - 7x32 = 1
Hence, by considering minimal solutions in x for D ≤ 7, the largest x is obtained when D = 5.
Find the value of D ≤ n in minimal solutions of x for which the largest value of x is obtained.
Information at Project Euler 066
Getting Started
Enter a whole number between 2 and 1000 (without leading zeros) and select the Submit Button. You will see the value of D for which the largest x is obtained, where D is less than or equal to the number entered. For example, if you entered 7, you would expect the value of D to be 5. If you have made an invalid input, you will get an error message. Select the Reset Button to clear the information or to start again.
User Stories
As a user, I expect to get an error message, if I do any of:
- Not enter anything in the input field
- Entering text other than a number
- Entering a number less than 2 or greater than 1000
- Including leading zeros such as 02
- Entering a number, but it is not an integer
As a user, if I select the Reset Button, I can clear the information or start again.
As a user, I expect the function diophantineEquation(7) to return a number.
As a user, I expect the function diophantineEquation(7) to return 5.
As a user, I expect the function diophantineEquation(100) to return 61.
As a user, I expect the function diophantineEquation(409) to return 409.
As a user, I expect the function diophantineEquation(500) to return 421.
As a user, I expect the function diophantineEquation(1000) to return 661.
User Stories on function diophantineEquation(n) taken from FreeCodeCamp - Coding Interview Prep - Project Euler 066
Information Architecture
The function diophantineEquation(n) returns a number, where n is a number between 2 and 1000.
Allows the user to enter a number in order to find the value of D less than or equal to that number in minimal solutions of x for which the largest value of x is obtained. Performs checks on valid user input. If the input is invalid, an error message is displayed.
Uses HTML5, CSS3, JavaScript with BigInt, Bootstrap 5.2.3 and Google Fonts.
Ensure all user stories have been met. Do a preview at:
python3 -m http.server
Select Open Preview or Open Browser. Input the values and Submit. Select the Reset Button - should allow the information to be cleared or to start again. If any or all the user stories have not been met, check typing. Press CTRL+C to quit.
Deployed on GitHub Pages at the main branch.
Written by me.