# How did this textbook go from this one step to the next? It's terribly confusing.

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?

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## 1 Answer

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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How am I reading it wrong? I copy and pasted what it says. –  Doug Smith Dec 16 '12 at 5:15
@DougSmith The statements $$-332 \equiv (1249-332) \pmod{1249} \equiv 917 \pmod{1249}$$ are intermediate statements and the actual equivalent statements are $$\color{red}{1 \equiv -332 \times 79 \pmod{1249}\\ \text{Equivalently} \\ 1 \equiv 917 \times 79 \pmod{1249}}$$ –  user17762 Dec 16 '12 at 5:17
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