a^iの7進法での1の位の周期を調べる

main.swift

func pow<Integer>(_ a: Integer, _ b: Integer, modulus: Integer?) -> Integer where Integer: BinaryInteger {
    var result: Integer = 1
    var a = a
    var b = b
    if let modulus = modulus {
        while true {
            if b & 0x1 != 0 {
                result = (result * a) % modulus
            }
            b >>= 1
            guard b > 0 else { break }
            a = (a * a) % modulus
        }
    } else {
        while true {
            if b & 0x1 != 0 {
                result *= a
            }
            b >>= 1
            guard b > 0 else { break }
            a *= a
        }
    }
    return result
}

var periods: Set<Int> = []
for a in 1 ... 10000 {
    var nn: Set<Int> = []
    for i in 1 ... 1000 {
        nn.insert(pow(a, i, modulus: 7))
    }
    print(a, nn.count)
    periods.insert(nn.count)
}
print(periods.sorted())