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**Lolz****Member**- Registered: 2017-07-30
- Posts: 4

Let m be a positive integer, and suppose that 9 is its own inverse (mod m), but 3 is not its own inverse (mod m). How many values for m are there?

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Deduce from the first statement that divides , which gives you a small number of possibilities to test against the second statement. ( of them, to be precise.)

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,322

Good morning zetafunc,

Are you assuming the operation is x; as in 9x9 = 81 ?

I had assumed the op is +

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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Hi Bob,

I was assuming that they meant the multiplicative inverse, yes -- if they meant additive inverse, the problem is very similar (though produces a different answer).

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**bob bundy****Administrator**- Registered: 2010-06-20
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hi

For + I'm getting two values; m=9 and m=18

What do you think?

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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Yes, I agree with that.

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