FediPrimes/lucas.py

# Finding lucas pseudoprimes
from math import sqrt, gcd

def isqrt(n):
    """ Find the integer square root of n via newton's method, code via
    stackoverflow:

    (https://stackoverflow.com/questions/15390807/integer-square-root-in-python)
    """
    x = n
    y = (x + 1) // 2
    while y < x:
        x = y
        y = (x + n // x) // 2
    return x

def hasIntSQRT(n):
    """Detect whether the square root of n is an integer,
    i.e. whether the isqrt(n) is the true square root.
    """
    isq = isqrt(n)
    return isq * isq == n

def Dsequence():
    """Generate sequence 5, -7, 9, -11, 13, -15...
    """
    val = 5
    while True:
        if val % 4 == 1:
            yield val
        else:
            yield -val
        val = val + 2

def Legendere(a, p):
    if (p % 2 == 0):
        raise ValueError("p must be odd, is {}".format(p))
    lv =  pow(a, (p-1)//2, p)
    if lv == p - 1:
        lv = -1
    return lv

def Jacobi(a, n):
    if (n % 2 == 0):
        raise ValueError("n must be odd, is {}".format(n))
    a = a % n
    mv = 1
    if (a % 2 == 0):
        a = a // 2
        nm8 = n % 8
        if (nm8 == 3 or nm8 == 5):
            mv = -1
    if n == 1:
        return mv * 1
    if gcd(a, n) != 1:
        return 0
    return mv * Jacobi(n, a)

for n in range(1, 21, 2):
    print("{}:\t{}".format(n, Jacobi(3, n)))