how would i solve

im getting confused around the mod 13 and finding its inverse would appreciate answer..exam revision!thanks

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- May 29th 2008, 01:29 PMskystarchinese remainder theorem
how would i solve

im getting confused around the mod 13 and finding its inverse would appreciate answer..exam revision!thanks - May 29th 2008, 01:35 PMMoo
- May 29th 2008, 02:08 PMgalactus
......[1]

......[2]

........[3]

From [1], we have

Sub into [2]:

Sub into x=3t+2, 3(8s+1)+2=24s+5

This must be an integer. That occurs first at**s=10**

By resubbing, we get 8(10)+1=82, 3(81)+2=245

**x=245**

We can check this and see it checks on our congruencies

(245-2)/3=81

(245-5)/8=30

(245-11)/13=18

Make sure I didn't go astray somewhere. Make sure this is the smallest. - May 29th 2008, 02:34 PMskystar
where did 3t+2 come from,,typo on [1]?

- May 29th 2008, 02:38 PMgalactus
I had 13 instead of 3 in the first one. Should be mod 3. I had mod 13

- May 29th 2008, 03:20 PMgalactus
Hey, check what I just found. I ran our problem through it and it checks

That reminds me, the solutions should be written as 245 mod 312. I just posted the smallest.

Section 7.3: Solving Lots of Congruences