Number properties

[versatile801]

Hi,

The question pertains to Number Properties. ( pg no 153, Q-5 )

what are the remainders upon division by 4 ?

Option B - the square of an ODD integer

Answer is - 1

Now the answer explanation says that Generic expression of an odd integer is 2n+1.

If we consider the above definition to suppose an odd number , we are missing 1 - which is an odd no itself.

In the same question, if i take odd no as 1 , the square of this odd no is 1 , and when divided by 4, it leaves 0 reminder

Pls explain, why generic expression of odd no is taken as 2n+1 ?

[tim]

How do you get an odd number? It’s one more than an even number. An even number is twice an integer, in other words 2n; so an odd number is 2n+1..

[versatile801]

Thanks tim.

But what about 1 then.. ??

1 is also odd no, it does not require 2n to be added to it, when we say 2n+1, it starts with no 3 and goes on.

So, how can we say generic expression of an odd no is 2n+1 ?

thanks

[stud.jatt]

Thanks tim.

But what about 1 then.. ??

1 is also odd no, it does not require 2n to be added to it, when we say 2n+1, it starts with no 3 and goes on.

So, how can we say generic expression of an odd no is 2n+1 ?

thanks

umm... lets try n = 0 shall we??

[tim]

Thanks, stud [sic]