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When I typed in

6^-1 mod 49 in Wolfram|Alpha, it gave me an answer of 41. Link here

If I type the same thing as (1/6) mod 49 , I don't see 41 any more. Why is this happening ?Link here

A Related question :

How is the answer to 6^-1 mod 49 , 41 in the first place ?

A small change in the above question :

If the question is find , 9^-2 mod 49, what are the steps to find the answer ?

  • 1
    You can use the extended Euclidean algorithm to find the modular inverse of $81$, $\bmod 49$. See [this](http://en.wikipedia.org/wiki/Modular_multiplicative_inverse).2012-07-20

1 Answers 1

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The $41$ is because $6\times 41=246=1\bmod 49$.

I assume that what's happening is that if you type $(1/6)$ instead, it assumes that you're happy to work with rational numbers rather than just integers and gives you back $1/6$.

  • 1
    In short: `Mod[1/6, 49]` and `PowerMod[6, -1, 49]` are two different things.2012-07-20