Thread: modulo ?

hi there I having some troble with a few problems i was wondering if i could get some help?

x^2 equvilent to -1 mod 19

x^2 equvilent to -1 mod 19

4x equvilent to 6 mod 15

thanks for your help

Originally Posted by bugal402

4x equvilent to 6 mod 15

thanks for your help

I'll defer the first too to more able number theorists.

this is solvable since . Now do you know how to solve Diophantine equations?


P.S. It might be easier to just guess :S

exists modulo .

You can find by the Euclidean algorithm.

I omit details but .

So

Originally Posted by bugal402

hi there I having some troble with a few problems i was wondering if i could get some help?

x^2 equvilent to -1 mod 19

x^2 equvilent to -1 mod 19


You asked twice the same......anyway, the equation has a solution iff , so in your case...

Tonio


4x equvilent to 6 mod 15

thanks for your help

.

Originally Posted by Drexel28

I'll defer the first too to more able number theorists.

this is solvable since . Now do you know how to solve Diophantine equations?


P.S. It might be easier to just guess :S

I know how to do Diophantine equations. thanks again

Originally Posted by tonio

.

you are right I did the second one was supposed to be x^2 equvilent to -1 mod 17

sorry about that

Originally Posted by tonio

.

So this one does not have a solution right?

Originally Posted by bugal402

So this one does not have a solution right?

The one for 19 hasn't , and the one for 17 has...and a pretty easy one, in fact.

Tonio