Multivariable equation in multiplicative group Z_p

asked 2017-09-29 15:19:36 +0200

dcole gravatar image

I am able to, in wolfram alpha, plug in the equation

11=x*(y^119)^149mod151

where all numbers are in Z_151

and wolfram is able to give me a set of non-zero solutions (x,y) that I think satisfy (11*y^119, y)

I have tried using symbolic equations and the sage quickstart for number theory to replicate this functionality, but I am getting stuck on some integer conversion TypeErrors in sage.

I have tried to set it up like:

x,y = var('x,y');

qe=(mod(x*(y^119)^149,151)==mod(11,151))

Can someone help me set up this equation, and then solve for all possible non-zero solutions?

THanks!

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For instance, typing

If we define `f` by

    def f(x, y):
        return (x, y)

then `f(2, 3)` returns `(2, 3)` but `f(2)` gives:

    TypeError: f() takes exactly 2 arguments (1 given)

will produce:

If we define f by

def f(x, y):
    return (x, y)

then f(2, 3) returns (2, 3) but f(2) gives:

TypeError: f() takes exactly 2 arguments (1 given)

Can you edit your question to do that?

slelievre gravatar imageslelievre ( 2017-09-30 19:29:27 +0200 )edit

Is this the same question as here?

https://ask.sagemath.org/question/39003/solving-two-variable-equations-mod-p/

dan_fulea gravatar imagedan_fulea ( 2017-09-30 23:50:06 +0200 )edit
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