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rune2402

Banned

Registered: 2007-10-23

Posts: 32

solutions ofr x congruency mod (6)

Solve the problem.
Find all positive solutions for the equation. x congruency 5(mod 6)

    a.     {5, 11, 17, ...} 
    b.     {11, 17, 78, ...} 
    c.     {5, 10, 15, ...} 
    d.     {11, 17, 23, ...}

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: solutions ofr x congruency mod (6)

If

This implies that x = 5 + 6k for some k.

Therefore the solution set is a.

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: solutions ofr x congruency mod (6)

Sorry . the answer is D because all three numbers leave the exact remainder of 5 when divided by the mod-6.They all leave 5 which is equal to the 5 shown.

At least that is what all the other forums say, but somehow i am not convinced. You may be right.

I've saved this to email.i'll be back with an explanation and the verified answer.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: solutions ofr x congruency mod (6)

Well, d. has all solutions except x=5. I would think you would also have to have 5 in your solution set, since it says ALL positive solutions, and not ALL OTHER positive solutions.

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: solutions ofr x congruency mod (6)

I see what your saying. it makes sense, but what is the answer.

Aha! The difference between 5 and the digits in answer D all divide by mod 6 with no remainder. Thus D is the answer because the other options include numbers that do not divide evenly.That is, they have remainders when divided by 6.

One integer n is said to be divisible by another integer m if m divides n with no remainder. So 14 is divisible by 7 but 15 is not.

Two integers m and n are said to be congruent modulo N (N also an integer) if their difference is divisible by N.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: solutions ofr x congruency mod (6)

The same goes for a...

6 | 11-5 = 6
6 | 17-11 = 6
6 | 17-5 = 12

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: solutions ofr x congruency mod (6)

You forgot 78.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: solutions ofr x congruency mod (6)

Ok, but set b. is missing several solutions between 17 and 78.

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: solutions ofr x congruency mod (6)

Ill save this untill I am more awake.Ill be back.