Discrete.swift

func gcd(x: Int, _ y: Int) -> Int {
    var a, b: Int
    if x > y { a = x; b = y }
    else { a = y; b = x }
    
    var remainder: Int
    
    repeat {
        remainder = a % b
        a = b
        b = remainder
    } while remainder != 0
    
    return a
}

gcd(945, 2415)

func lcm(x: Int, _ y: Int) -> Int {
    return x * y / gcd(x, y)
}

lcm(945, 2415)

infix operator ** { associativity left precedence 170 }
func **(base: Int, power: Int) -> Int {
    var product = 1
    for _ in 0..<power {
        product *= base
    }
    return product
}

let a: Int = 3, b: Int = 4
a ** b

func representInBase(x: Int, base: Int) -> String {
    var result = ""
    var currentNumber = x
    let digits = ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z"]
    
    if base < 1 || base >= digits.count {
        fatalError("Base must be greater than 0 and less than \(digits.count)")
    }
    
    if currentNumber < 0 {
        result = "-"
        currentNumber = -currentNumber
    }
    
    var index = 0
    if base > 1 {
        while base ** index <= currentNumber {
            index += 1
        }
        index -= 1
    
        while index >= 0 {
            var digit = 0
            while digit * base ** index <= currentNumber {
                digit += 1
            }
            digit -= 1
            result += "\(digits[digit])"
            currentNumber -= digit * base ** index
            index -= 1
        }
    } else if base == 1 {
        for _ in 0..<currentNumber {
            result += "1"
        }
    }
    
    return result
}

representInBase(6253584, base: 12)