LINEAR DIOPHANTINE EQUATIONS

The Python function isolve(a,b,c) produces an integer
solution of the equation

   ax + by = c,
   
where a, b, and c are integers.  It is assumed that
the equation is solvable, i.e., that c divides
the gcd of a and b.  Otherwise its output is not
correct.  The solution is found recursivley  using t
the Euclidean algorithm.

EXAMPLE:

  >>> isolve(1234,4321,1)
  [-1082, 309]

Note that divmod(a,b) returns a tuple consisting
of the quotient and remainder computed when a is
divided by b.  Thus divmod(17,3) = (5,2)


----------------------------------------------------

def isolve(a,b,c):
  """isolve(a,b,c): return solution of ax + by = c.  
  Recursive implementation."""
  qr = divmod(a,b)
  q = qr[0]
  r = qr[1]
  if r == 0:
    return( [0,c/b] )
  else:
    sol = isolve( b, r, c )
    u = sol[0]
    v = sol[1]
    return( [ v, u - q*v ]