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## #1 2017-09-03 11:38:29

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

### Help FAST!

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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## #2 2017-09-03 19:52:48

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,100
Website

### Re: Help FAST!

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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## #3 2017-09-03 20:07:54

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,108

### Re: Help FAST!

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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## #4 2017-09-03 20:22:46

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,100
Website

### Re: Help FAST!

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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## #5 2017-09-03 22:42:07

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,108

### Re: Help FAST!

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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## #6 2017-09-03 22:49:05

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,100
Website

### Re: Help FAST!

Yes, I agree with that.

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