Question

x=2(mod 3)
x=3(mod 7)
x=7(mod 5)

find a unique incongruent solution to modulo n.

(number theory problem using chinese remainder theorem)

please help!!

Answer 1

Yes this is indeed a basic application of CRT, you want me to do it for you?

Answer 2

that would be nice11

Answer 3

\[ x=17 \]

Answer 4

i don't think so.. because based on the book, the answer would be in the pattern
a=b(mod n)

Answer 5

Use your head man, this is elementary.

Answer 6

First, check if there was a typo in the question, x=7(mod5) doesn't not sound right.
Will proceed as if it were x=2(mod5). Method does not change.

The basic requirement is to satisfy all conditions
x=2(mod 3)
x=3(mod 7)
x=2(mod 5)
We realize that there are infinitely many solution, all of which satisfy all three conditions.
Suppose 17 is one such solution [check: 17=2(mod3), 17=3(mod7), 17=2(mod5), OK].

We calculate the LCM of 3,7 and 5 to be 3*7*5=105. In other words, 105 has a remainder of 0 when divided by 3, 7 or 5.

Hence 17 mod 105 is a general solution to the above problem, since if we add multiples of 105 to 17, the remainder will not change.

Answer 7

"First, check if there was a typo in the question, x=7(mod5) doesn't not sound right.
Will proceed as if it were x=2(mod5). " --- Why?

As far as I can see (3,4,5)=1 so perfect candidate for CRT.

Answer 8

I suspected a typo because we don't usually write x=7(mod5) where 7>5.

Answer 9

That's true :)

Answer 10

:)