Multiply every other digit by 2, starting with the number’s second-to-last digit, and then add those products’ digits together.
Add the sum to the sum of the digits that weren’t multiplied by 2.
If the total’s last digit is 0 (or, put more formally, if the total modulo 10 is congruent to 0), the number is valid!

For the sake of discussion, let’s first underline every other digit, starting with the number’s second-to-last digit:

4003600000000014

Okay, let’s multiply each of the underlined digits by 2:

1•2 + 0•2 + 0•2 + 0•2 + 0•2 + 6•2 + 0•2 + 4•2

That gives us:

2 + 0 + 0 + 0 + 0 + 12 + 0 + 8

Now let’s add those products’ digits (i.e., not the products themselves) together:

2 + 0 + 0 + 0 + 0 + 1 + 2 + 0 + 8 = 13

Now let’s add that sum (13) to the sum of the digits that weren’t multiplied by 2 (starting from the end):

13 + 4 + 0 + 0 + 0 + 0 + 0 + 3 + 0 = 20

Yup, the last digit in that sum (20) is a 0, so David’s card is legit!

package main

import (
    "fmt"
    "strconv"
)

// 4003600000000014 - VISA
// it doesn't use arrays or struct
// pure mathematic solution

func main() {
    // get card number
    var cardNumber int = -1
    for cardNumber == -1 {
        cardNumber = getCardNumer()
    }

    // get the number of digits from the card
    numDigits := getNumberDigitsCard(cardNumber)

    // AUX VARIABLES ---------------------------
    // aux vars for iterate through the card number
    mod := 10
    divider := 1
    // aux for know the ieration, because it goes from right to left
    var generalOdd bool = (numDigits % 2) != 0
    // aux var for iterate one yes - one no
    odd := generalOdd
    // accumulators
    ac1 := 0 // special - the one that will be multiple by 2
    ac2 := 0 // odds - start from the second digit

    // ITERATE CARD NUMBER
    for cardNumber > divider {

        // get the digit from the right
        var currentVal int = (cardNumber % mod) / divider

        // move one digit to the left
        mod = mod * 10
        divider = divider * 10

        // LOGIC FROM Hans Peter Luhn ALGORITHM
        // make the sum step from digits
        if odd {
            if !generalOdd {
                ac1 = ac1 + specialSum(currentVal)
            } else {
                ac1 = ac1 + currentVal
            }
        } else {
            if generalOdd {
                ac2 = ac2 + specialSum(currentVal)
            } else {
                ac2 = ac2 + currentVal
            }
        }
        odd = !odd
    }
    var result int = ac1 + ac2

    // CHECK THE RESULT
    // compare the info given from the credit cards
    var cardType string = checkResult(result, numDigits, cardNumber)
    fmt.Println(cardType)
}

func getCardNumer() int {
    // get the value
    var str string = ""
    fmt.Print("Enter a card number: ")
    fmt.Scanf("%s", &str)

    // convert value
    cardNumber, err := strconv.Atoi(str)

    // handle error if no number was provided
    if err != nil {
        fmt.Println("Enter only numbers")
        return -1
    }

    return cardNumber
}

func getNumberDigitsCard(card int) (numDigits int) {
    divider := 10
    // because is an int, will delete the decimals from each division
    for card != 0 {
        card = card / divider
        numDigits += 1
    }
    return
}

// SPECIAL SUM
// because the log says if multiple by 2 is equal to a number with two digits
// we should sum the two digits from the number
func specialSum(num int) int {
    if num < 5 {
        return num * 2
    } else {
        num = num * 2
        var n1 int = num % 10
        var n2 int = num / 10
        return n1 + n2
    }
}

// CHECK THE RESULT
// compare the info given from the credit cards
func checkResult(result, numDigits, cardNumber int) string {
    if (result % 10) == 0 {
        var divisor int = 1
        for i := 0; i < numDigits-2; i++ {
            divisor = 10 * divisor
        }
        var firstDigits int = cardNumber / divisor
        var firstDigit = firstDigits / 10
        if firstDigits == 34 || firstDigits == 37 {
            if numDigits == 15 {
                return "AMEX"
            } else {
                return "INVALID"
            }
        } else if firstDigits == 51 || firstDigits == 52 || firstDigits == 53 || firstDigits == 54 || firstDigits == 55 {
            if numDigits == 16 {
                return "MASTERCARD"
            } else {
                return "INVALID"
            }
        } else if firstDigit == 4 {
            if numDigits == 13 || numDigits == 16 {
                return "VISA"
            } else {
                return "INVALID"
            }
        }
    }
    return "INVALID"
}