Num Prop: 4th Ed Page 148 Rep Even and Odds Algebraically

[ekshamatha]

What is the remainder when a is divided by 4?
(1) a is a square of an odd integer.
(2) a is a multiple of 3.

2n+1 is considered as the odd integer so (2n+1)^2

(1) will have a remainder of 1 - SUFFICIENT
(2) Insufficient.

What i do not understand is if i consider the odd integer as 2n-1
then (2n-1)^2 => if n = 1 then a = 1 , but if n = 2 then a = 9 then the remainder would be 1. Could any one please explain me why we should consider 2n+1 only and not 2n-1 for 'a'.

[messi10]

Hi,

Not sure if I see a problem with 2n-1. Even with a=1 the remainder is still 1. 4 goes 0 times to give 0 and you get remainder 1.

Regards

Sunil

[ekshamatha]

thanks! i missed the point of 0 and the remainder to be 1.

[jnelson0612]

Thanks Sunil!