n,n+4 n+12and n+16 is devisle by 5 where is any positive integer solution
Answers
Hey there !!
Any positive integer is of the form 5q , 5q + 1 , 5q + 2
here ,
b = 5
r = 0 , 1 , 2 , 3 , 4
when r = 0 , n = 5q
n = 5q ----> divisible by 5 ===> [1]
n + 4 = 5q + 4 [ not divisible by 5 ]
n + 6 = 5q + 6 [ not divisible by 5 ]
n + 12 = 5q + 12 [ not divisible by 5 ]
-------------------------------------------
when r = 1 , n = 5q + 1
n = 5q + 1 [ not divisible by 5 ]
n + 4 = 5q + 5 = 5 [q+ 1] ----> divisible by 5 ===> [2]
n + 6 = 5q + 7 [ not divisible by 5 ]
n + 12 = 5q + 13 [ not divisible by 5 ]
----------------------------------------
when r = 3 , n = 5q + 3
n = 5q + 3 [ not divisible by 5 ]
n + 4 = 5q + 7 [ not divisible by 5 ]
n + 8 = 5q + 11 [ not divisible by 5 ]
n + 6 = 5q + 9 [ not divisible by 5 ]
n + 12 = 5q + 15 = 5 [ q + 3 ] ---> divisible by 5 ====> [3]
----------------------------------------------------
when r = 4 , n = 5q + 4
n = 5q + 4 [ not divisible by 5 ]
n + 4 = 5q + 8 [ not divisible by 5 ]
n + 6 = 5q + 10 = 5 [ q + 2 ] ---> divisible by 5 ====> [4]
n + 12 = 5q + 16 [ not divisible by 5 ]
from 1 , 2 , 3 , 4 its clear that one and only one out of n, n+4, , n+12 and n+6 is divisible by 5