Question

Credit card numbers follow certain patterns. A credit card number must have between 13 and 16 digits. It must start with 4 for Visa cards, 5 for Master cards, 37 for American Express cards, and 6 for Discover cards. In 1954, Hans Luhn of IBM proposed the following algorithm for validating credit card numbers:

a. Double every second digit from right to left (e.g., if number is 3 => 3 * 2 => 6) and add them together.

b. If this doubling results in a two-digit number, then add the two digits to get a single-digit number (e.g., if number is 5 => 5 * 2 => 10 => 1+0 => 1).

So, for the credit card number 4388576018402626, doubling all second digits from the right results in (2 * 2 = 4) + (2 * 2 = 4) + (4 * 2 = 8) + (1 * 2 = 2) + (6 * 2 = 12 = 1 + 2 = 3) + (5 * 2 = 10 = 1 + 0 = 1) + (8 * 2 = 16 = 1 + 6 = 7) + (4 * 2 = 8).

This totals to 4 + 4 + 8 + 2 + 3 + 1 + 7 + 8 = 37. Add all digits in the odd places from right to left.

The leftmost digit of the credit card number is at index 0; 6 + 6 + 0 + 8 + 0 + 7 + 8 + 3 = 38.

Add results from steps (a) and (b) and see if divisible by 10. If it is, then the card number is valid; otherwise invalid. 37 + 38 = 75 is not divisible by 10, so it is an invalid credit card number.

Implement Luhn's algorithm in a program to determine whether a given credit card number is valid or not. You must test if the number of digits in the input is in the valid range (13 to 16), run Luhn's algorithm to test its validity, and if it is valid, print the name of the company that offers that credit card number.