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copied!<p>You might also want to look at the <a href="http://code.google.com/p/gmpy/" rel="nofollow noreferrer">gmpy</a> module. It is an interface between Python and the GMP multiple-precision library. gmpy provides an invert function that does exactly what you need:</p> <pre><code>>>> import gmpy >>> gmpy.invert(1234567, 1000000007) mpz(989145189) </code></pre> <p><strong>Updated answer</strong></p> <p>As noted by @hyh , the <code>gmpy.invert()</code> returns 0 if the inverse does not exist. That matches the behavior of GMP's <code>mpz_invert()</code> function. <code>gmpy.divm(a, b, m)</code> provides a general solution to <code>a=bx (mod m)</code>.</p> <pre><code>>>> gmpy.divm(1, 1234567, 1000000007) mpz(989145189) >>> gmpy.divm(1, 0, 5) Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: not invertible >>> gmpy.divm(1, 4, 8) Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: not invertible >>> gmpy.divm(1, 4, 9) mpz(7) </code></pre> <p><code>divm()</code> will return a solution when <code>gcd(b,m) == 1</code> and raises an exception when the multiplicative inverse does not exist.</p> <p>Disclaimer: I'm the current maintainer of the gmpy library.</p> <p><strong>Updated answer 2</strong></p> <p>gmpy2 now properly raises an exception when the inverse does not exists:</p> <pre><code>>>> import gmpy2 >>> gmpy2.invert(0,5) Traceback (most recent call last): File "<stdin>", line 1, in <module> ZeroDivisionError: invert() no inverse exists </code></pre>

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