I just noticed in Integer, too, the invert method which gives the
multiplicative inverse mode n of a number:

>>> invert(S(3),5)
2
>>> (3*2)%5 == 1
True
>>> invert(S(4),6)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "sympy\polys\polytools.py", line 4249, in invert
    return f.invert(g)
  File "sympy\core\numbers.py", line 1322, in invert
    raise ZeroDivisionError("zero divisor")
ZeroDivisionError: zero divisor

To find an Integer given a description of it's modulus profile perhaps
a method "from_moduli" could be added so Integer.from_moduli((2, 3),
(3, 5)) would give 8. Hector, Mateusz, anyone else: does that look
like a good way to construct it? Is there a better method name?

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