Math Is Fun Forum

Lolz

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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?

zetafunc

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Registered: 2014-05-21

Posts: 2,440

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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.)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zetafunc

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Registered: 2014-05-21

Posts: 2,440

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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).

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: Help FAST!

Yes, I agree with that.