Question

Prove that odd number is not divisible by 4.

Answer 1

any odd number can be represented as (2n+1). So, (2n+1)/4=2n/2^2+1/2^2.

Answer 2

1/2^2 Always remains as a remainder, even if 2n is fully divisible.

Answer 3

thanks =)

Answer 4

you can prove it this way.
by contradiction, assume there exist an odd number divisible by 4.
this means

2k+1 = 4*n
but this can be rewritten
2k + 1 = 2 (2n)

therefore we get that an odd number is equal to an even number . this is absurd!

Answer 5

so no odd numbers are divisible by 4

Answer 6

@perl : Nice idea!

Answer 7

or even shorter proof ,
if any odd number is divisible by 4, then that odd number is also divisible by 2 (since 4 is even) . but an odd number being divisible by 2 means an odd number is even (which is ludicrous ) . so there cannot be any odd number divisible by 4.

Answer 8

you can prove that no odd number is equal to even number. odd number is written as 2k+1 and even number is written 2n. and 2k+1 = 2n has no solution

Answer 9

Thanks alot =D