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# Number Systems and Divisibility

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1. I am currently tackling questions of the form:
if n exists in the integers, then 7 divides one of the following:

n-4,n+2,n+5,n+6,n+11,n+14. True or False?

I have the answer to this which tells me to divide each term by 7 and find the remainders, which are:

n+3,n+2,n+5,n+6,n+4,n

but I have no idea where these values have come from? Could anybody tell me where this comes from? Or provide me with a different method for solving this
2. (Original post by gdickinson_)
I am currently tackling questions of the form:
if n exists in the integers, then 7 divides one of the following:

n-4,n+2,n+5,n+6,n+11,n+14. True or False?

I have the answer to this which tells me to divide each term by 7 and find the remainders, which are:

n+3,n+2,n+5,n+6,n+4,n

but I have no idea where these values have come from? Could anybody tell me where this comes from? Or provide me with a different method for solving this
Hey I've moved this question to maths study help for you.

Have you studied modular arithmetic?
3. (Original post by gdickinson_)
I am currently tackling questions of the form:
if n exists in the integers, then 7 divides one of the following:

n-4,n+2,n+5,n+6,n+11,n+14. True or False?

I have the answer to this which tells me to divide each term by 7 and find the remainders, which are:
Look at modular arithmetic , since so dividing by 7 leaves a remainder of 4. since there is no remainder .
4. (Original post by Zacken)
Look at modular arithmetic , since so dividing by 7 leaves a remainder of 4. since there is no remainder .
Hi, yes I am currently studying modular arithmetic. I under stand the examples you have given me but I can't make sense of my original question. Where does n come into it? What is n?
5. (Original post by gdickinson_)
Hi, yes I am currently studying modular arithmetic. I under stand the examples you have given me but I can't make sense of my original question. Where does n come into it? What is n?
is just any integer.
6. I see now! Is there any chance you can help me with 8 divides [2n], having the values {0,2,4,6}. I understand that 8 divides [n] gives {0,1,2,3,4,5,6,7}
7. (Original post by gdickinson_)
I see now! Is there any chance you can help me with 8 divides [2n], having the values {0,2,4,6}. I understand that 8 divides [n] gives {0,1,2,3,4,5,6,7}
Is this a different problem? What does the square brackets represent?

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