Loser66
  • Loser66
What is wrong? Solve \(13x \equiv 6 (mod 15) Please, help
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Loser66
  • Loser66
That is 13x -15y = 6 gcd (13, 15) =1 and 1 | 6, hence there is a solution 15 = 13 +2 , then 2 = 15 -13 13 = (7) 2 + 1, then 1 = 13 -(7) 2 = 13-(7) (15-13) = (8) 13 -(7) 15 multiple both sides by 6 13(48) - 15(42) =6 Hence x = 48 mod 15, or \(x \equiv 3 (mod 15)\)
Loser66
  • Loser66
Now, crazy thing comes. if I take x = 18, then \(x\equiv 3 (mod 15)\) then x =18 is one of the solution, right? Plug back to original one 13*18 = 234 \(\equiv 9 (mod 15)\) not 6 as required. :(
Loser66
  • Loser66
@superdavesuper

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Loser66
  • Loser66
@IrishBoy123
Loser66
  • Loser66
But if I stop at 2 = 15 -13, I am ok, since 6 = 15 (3) + 13( -3) Hence \(x \equiv -3\equiv 12 (mod 15)\) Test back , take x =12, then 13 * 12 = 156 \(\equiv 6 (mod 15)\) I don't know what is wrong with the first one.
superdavesuper
  • superdavesuper
how about simple typo... " 15 = 13 +2 , then 2 = 15 -13 13 = (7) 2 + 1, then..." second line should be 13 = (6)2 + 1 going down dat path, u will get 12 (mod 15) as the right ans :D
Loser66
  • Loser66
damn!! silly mistake. Thank you so much

Looking for something else?

Not the answer you are looking for? Search for more explanations.