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The PDF (it's small) is available here: http://www.cc.gatech.edu/~mihail/2050Lec10.pdf

It says:

1 ≡ −332×79 mod 1249

Equivalently, since:

−332≡(1249−332) mod1249

How did they get that equivalency? How do you jump from that first equation to the next?

1 Answers 1

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You are reading it incorrectly, what it says the following.

$\color{red}{1 \equiv -332 \times 79 \pmod{1249}\\ \text{Equivalently} \\ 1 \equiv 917 \times 79 \pmod{1249}}$

To prove that the two statements are equivalent, it uses the fact that $-332 \equiv (1249-332) \pmod{1249} \equiv 917 \pmod{1249}$

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    @DougSmith The statements $-332 \equiv (1249-332) \pmod{1249} \equiv 917 \pmod{1249}$ are intermediate statements and the actual equivalent statements are $\color{red}{1 \equiv -332 \times 79 \pmod{1249}\\ \text{Equivalently} \\ 1 \equiv 917 \times 79 \pmod{1249}}$2012-12-16