the remainder ???

[ikhlas]

I missed the first question:
so when n is divided by 7 the remainder is 5 so
n = 7k + 5
but we need 2n so we multiply by 2
2n = 14k + 10
factor out 7...
2n = 7(2k) + 10
==> the remainder when 2n is divided by 7 is 10

great job metodiev ! many thanks , i get now the idea from the remainde
ikhlas

[300IS]

I missed the first question:
so when n is divided by 7 the remainder is 5 so
n = 7k + 5
but we need 2n so we multiply by 2
2n = 14k + 10
factor out 7...
2n = 7(2k) + 10
==> the remainder when 2n is divided by 7 is 10

So this is not the correct answer

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n is div by 7 remainder is 5 , so

the equation for this is

n=7*x+5.

if u take x=1

n=12.

then 2n/7= 2*12/7= 24/7 , remainder is 3

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Also, for the picture question, I did it this way. Please correct me if i am wrong in my math logic.

the reminder when n is divided by 3 is 1 , and the reminder when n+1 is divided by 2 is 1 .

what is the reminder when n-1 is divided by 6

So, I did it like this.
n = 3k + 1
plug in k = 1

n = 3(1) + 1 => 4

n+1 = 2k + 1 => n = 2k = 2 since k = 1 (plug in)

So, the answer says its n-1, so i just go 4-1 = 3
and also by the 2nd equation, n = 2 when n + 1, so. n + 1 = 2 + 1 = 3. both agree... ok.. maybe this is wrong..


but for your math, why do you let k = 2j + 1. Thanks.

[metodiev]

Thanks for pointing this out , I did this quickly and forgot to factor out 7
so we have n = 7k + 5
and 2n = 14k + 10 (of course the remainder cannot be 10 when 2n is divided by 7, the remainder can never be greater than or equal to the divisor - silly me!)
2n = 14k + 7 + 3
2n = 7(2k+1) + 3 ==> the remainder is 3

but for your math, why do you let k = 2j + 1. Thanks.

OK, n = 2m ==> n is even number (m is integer)
n = 3k + 1
==> 3k + 1 must be even
==> 3k must be odd and only a product of odd*odd=odd
in general you represent odd numbers in the form of 2k+1 since you are sure it is odd for any integer

[300IS]

OK, n = 2m ==> n is even number (m is integer)
n = 3k + 1
==> 3k + 1 must be even
==> 3k must be odd and only a product of odd*odd=odd
in general you represent odd numbers in the form of 2k+1 since you are sure it is odd for any integer

oh no no, Ididnt point it out, because I thought I got it wrong again.


2) Ahhh.. I now understand where you're coming from.. and how you get the remainder = 3.

Thanks again