Posted by **yin** on Wednesday, November 28, 2012 at 10:48am.

Solve the congruence 24x identical to 42 (mod 30) for x. List all the solutions (if there are any).

- Proofs and numbers -
**Reiny**, Wednesday, November 28, 2012 at 12:35pm
24x = 42 mod 30

24x = 12 mod 30

(24-30)x = 12 mod 30

-6x = 12 mod 30

x = -2

so one possible solution is x = -2(24) = -48

adding/subtracting multiples of 30 , our mod, will yield other solutions

making -2(24) + 60 , or 12 , our smallest positive answer

A general solution would be **12 + 30k**, where k is an integer

check:

look at the sequence of numbers

... -108 - 78 - 48 -18 12 42 72 102 ...

IF we take 102 30 we get

3 + 12/30

or

2 + 42/30

so clearly we can see that 102 = 12 mod 30 = 42 mod 30

## Answer this Question

## Related Questions

- Proofs and numbers - Prove the following theorem: Suppose p is a prime number, r...
- Math - Consider the congruence 6x=15(mod 21). How many solutions does the ...
- Math - Which Statements of congruence are true and which are false and why? 177 ...
- math - Which Statements of congruence are true and which are false and why? 177 ...
- Math - Which Statements of congruence are true and which are false and why? 177 ...
- math - Which two is true as i'm confused A) 3+7 10 mod 15 17 + 9 4 mod 21 ...
- Math - What are the 3 solutions? I'm stuck! 6x=15(mod 21) a=6,m=21,b=15 d=gcd(6,...
- algebra - Did I do this problem the correct way if so is there a shorter way to ...
- Data Structures and Algorithms - Given integers R,M with M≠0, let S(R,M) ...
- alg2 check? - solve 3(8x-2)=46-2(12x+1) 24x-6=46-24x+2 24x-6=48-24x 48x-6=48 48x...