Question

Hey!
Plz guide me, what to do now?..
(with complete explanation )

Answer 1

Let a = bq+r,

Where q = 5, => 0≤r<5, and let b = m

Possibilities of r and a are,

a = 5m, if r= 0,
a = 5m+1 , if r = 1,
a = 5m+2 , if r = 2,
a = 5m+3, if r = 3,
a = 5m+4 , if r = 4,


Now, Supposing m is an odd number as per the question (Posted in the comments)

We know that,
Odd x Odd = Odd,
Odd + Odd = Even,
Odd + Even = Odd,

Here 5m is always even if m is odd,

Now all we have to do is add an odd Integer to make it even,

Which are , 1,3 in this case,

=> 5m+1 and 5m+3 are always even if m is odd,

Therefore, Hence proved that 5m+1 and 5m+3 are always even if m is odd !.

Note : You might wonder why I have done this, But remember that if the question is to prove some linear thing, Go with the question,

There is no need for doing square of these, You have to do it only when they ask "prove square of......." , If the question doesn't contain that, take q and b as what's given in the question !.

Hope you understand, Have a great day !.
Thanking you, Bunti 360 !.