(a, b, c)
return a, b, c
Transform the equation `ax^2 + by^2 + cz^2 = 0` to an equivalent equation
    `a'x^2 + b'y^2 + c'z^2 = 0` with `\gcd(a', b') = 1`.

    Returns a tuple `(a', b', c')` which satisfies above conditions. Note that
    in the returned tuple `\gcd(a', c')` and `\gcd(b', c')` can take any value.

    Examples
    ========

    >>> from sympy.solvers.diophantine import make_prime
    >>> make_prime(4, 2, 7)
    (2, 1, 14)

    See Also
    ========

    pairwaise_prime(), reconstruct()
Transform the equation `ax^2 + by^2 + cz^2 = 0` to an equivalent equation
    `a'x^2 + b'y^2 + c'z^2 = 0` with `\gcd(a', b') = 1`.
Transform the equation ax^2 + by^2 + cz^2 = 0 to an equivalent equation a x^2 + b y^2 + c z^2 = 0 with \ gcd ( a b ) = 1 .
def make_prime(a, b, c):
    """
    Transform the equation `ax^2 + by^2 + cz^2 = 0` to an equivalent equation
    `a'x^2 + b'y^2 + c'z^2 = 0` with `\gcd(a', b') = 1`.

    Returns a tuple `(a', b', c')` which satisfies above conditions. Note that
    in the returned tuple `\gcd(a', c')` and `\gcd(b', c')` can take any value.

    Examples
    ========

    >>> from sympy.solvers.diophantine import make_prime
    >>> make_prime(4, 2, 7)
    (2, 1, 14)

    See Also
    ========

    pairwaise_prime(), reconstruct()
    """
    g = igcd(a, b)

    if g != 1:
        f = factorint(g)
        for p, e in f.items():
            a = a // p**e
            b = b // p**e

            if e % 2 == 1:
                c = p*c

    return a, b, c
def make_prime ( a , b , c ) : g = igcd ( a , b ) if g != 1 : f = factorint ( g ) for p , e in f . items ( ) : a = a // p ** e b = b // p ** e if e % 2 == 1 : c = p * c return a , b , c