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Number Systems and Divisibility

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
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. :smile:

Have you studied modular arithmetic?
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Zacken
22
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 −4≡3(mod7)-4 \equiv 3 \pmod{7}, 11≡4(mod7)11 \equiv 4 \pmod{7} since 11=7+411 = 7 + 4 so dividing by 7 leaves a remainder of 4. 14≡0(mod7)14 \equiv 0 \pmod{7} since there is no remainder 14=2×714 = 2\times 7.
Reply 3
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gdickinson_
OP
1
Original post by Zacken
Look at modular arithmetic −4≡3(mod7)-4 \equiv 3 \pmod{7}, 11≡4(mod7)11 \equiv 4 \pmod{7} since 11=7+411 = 7 + 4 so dividing by 7 leaves a remainder of 4. 14≡0(mod7)14 \equiv 0 \pmod{7} since there is no remainder 14=2×714 = 2\times 7.


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?
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Zacken
22
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?


nn is just any integer.
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gdickinson_
OP
1
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}
Reply 6
Avatar for Zacken
Zacken
22
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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