Question

Hey!!

4. Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.

Standard:- 10

Content Quality Solution Required

No Spamming otherwise reported on the spot

Answer 1

Here the nos. are....n,n+4,n+8,n+12 and n+16 which are composite nos.(This will be the prove that in the eucilid's chapter)....
So the value of n comes everytime the odd one...
n=1....equation n+4 gives 5
n=3....equation n+12 gives 15
n=5....equation n gives 5
n=7....equation n+8 gives 15
n=9....equation n+16 gives 25
and so on the result will be divisible by 5....

Answer 2

Given numbers are n,n + 4, n + 8, n + 12, n + 16.

Here n can be of the form of 5p, 5p + 1, 5p + 2, 5p + 3, 5p + 4.

1st case:

= > 5p, 5p + 4, 5p + 8, 5p + 12, 5p + 16.

5p is divisible by 5.


2nd case: 

= > 5p + 1, 5p + 5, 5p + 13, 5p + 17, 5p + 21

5p + 1 is divisible by 5.


3rd case:

= > 5p + 2, 5p + 6,5p + 10, 5p + 14, 5p + 18, 

5p + 10 is divisible by 5.


4th case:

= > 5p + 3, 5p + 7, 5p + 11, 5p + 15, 5p + 19.

5p + 15 is divisible by 5.


5th case:

= > 5p + 4, 5p + 8, 5p + 12, 5p + 16, 5p + 20

5p + 20 is divisible by 5.


Therefore n, n + 4, n + 8, n + 12, n + 16 is divisible by 5.


Hope this helps!