Hi I have a little question which I have partly tried but I am not completely sure if I am doing it correctly.

Heres the question

Does the equation 2x=26(mod32) have any solutions? If it does determine them and if not then explain why.

Down below is how I approached it: -

2x=26(mod32)

2x-26=32k

x-13=16k

therefore x=16k+13

This is where I get stuck, I don't know which values to use for K to give the final solutions for x.

Can anyone help me.

Mus.

4
Contributors
3
Replies
4
Views
13 Years
Discussion Span
Last Post by thoughtcoder

Hi I have a little question which I have partly tried but I am not completely sure if I am doing it correctly.

Heres the question

Does the equation 2x=26(mod32) have any solutions? If it does determine them and if not then explain why.

Down below is how I approached it: -

2x=26(mod32)

2x-26=32k

x-13=16k

therefore x=16k+13

This is where I get stuck, I don't know which values to use for K to give the final solutions for x.

Can anyone help me.

Mus.

You've completely solved the problem. Congratulations!. Any integer value of k gives a solution. for instance, k= 0 gives the solution x = 13. This is a solution because the statement 2*13 = 26 mod 32 is true. k = 1 gives the solution x = 29, etc. You could write the general solution as you have, x=13+16k, or you could write the general solution as x = 13 mod 16.

Hi Mus,

I think the first answer is 29 because 2x29-26=32

Moshi