theory number problem

[LIV]

N divided by 7, leaves remainder of 4. N^2 +5 divided by 7, remainder is?

[shwetarulzz]

The remainder will be 0. Please post the answer too.

[LIV]

Ans is 0. Please elaborate

[shwetarulzz]

Let Q be the quotient when N is divided by 7.

7Q + 4 = N

Now it says N is squared and 5 is added. ie - N^2 + 5 this can be written as (7Q + 4)^2 + 5.

We can expand this as (a+b)^2.
(7Q + 4)^2 + 5 = 49Q+14Q+16+5

Here remainder is 16+5 = 21. So when this number is divided by 7 since 21 is a multiple of 7 we dont end up with any remainder.

Hence - 0.

[shwetarulzz]

If u find this diff to follow take N to be say - 18.

18/ 7 --> Q : 2, R : 4

Now N^2 + 5 = 324 + 5 = 329.

329/7 gives Q: 47, R :0

Hope u understood.

[LIV]

thank quite simple gosh, I think I will rest now lol