def linear_congruence(a, b, m):
"""
Returns the values of x satisfying a*x congruent b mod(m)
Here m is positive integer and a, b are natural numbers.
This function returns only those values of x which are distinct mod(m).
Examples
========
>>> from sympy.polys.galoistools import linear_congruence
>>> linear_congruence(3, 12, 15)
[4, 9, 14]
There are 3 solutions distinct mod(15) since gcd(a, m) = gcd(3, 15) = 3.
**Reference**
1) Wikipedia http://en.wikipedia.org/wiki/Linear_congruence_theorem
"""
from sympy.polys.polytools import gcdex
if a % m == 0:
if b % m == 0:
return range(m)
else:
return []
r, _, g = gcdex(a, m)
if b % g != 0:
return []
return [(r * b // g + t * m // g) % m for t in range(g)]
def linear_congruence(a, b, m):
"""
Returns the values of x satisfying a*x congruent b mod(m)
Here m is positive integer and a, b are natural numbers.
This function returns only those values of x which are distinct mod(m).
Examples
========
>>> from sympy.polys.galoistools import linear_congruence
>>> linear_congruence(3, 12, 15)
[4, 9, 14]
There are 3 solutions distinct mod(15) since gcd(a, m) = gcd(3, 15) = 3.
**Reference**
1) Wikipedia http://en.wikipedia.org/wiki/Linear_congruence_theorem
"""
from sympy.polys.polytools import gcdex
if a % m == 0:
if b % m == 0:
return range(m)
else:
return []
r, _, g = gcdex(a, m)
if b % g != 0:
return []
return [(r * b // g + t * m // g) % m for t in range(g)]