Question

Show thatone and only one of ñ,n+4,n+8,n+12,andn+16 is divisible by 5, where n is any positive integer

Answer 1

If you know a bit of number theory, then this the is the most simple question of all possible questions!!!

Now there are 5 cases possible for n.
$n = 5k + r$
, where r can be any number from 0 to 4.
Now if r is 0, then n is a multiple of 5 and thus the statement holds true.
If r is 1, then n+4 is a multiple of 5 since the overall remainder will be 0.

Similarly, if r is 2, then n+8 is a multiple of 5.
If r is 3, then n+12 is a multiple of 5.
If r is 4, then n+16 is a multiple of 5.