The inverse of 3 module 7 is
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"The Euclidean algorithm ends quickly when used to find the greatest common divisor of 3 and 7.
7 = 2 x 3 + 1
From this equation we see that
-2 x 3 + 1 x 7 = 1
This shows that -2 is an inverse of 3 modulo 7. "
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