Question

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

Answer 1

Given that one and only one of n, n+4,n+8 ...is divisible by 5 where n is any positive integer
n+4 = 1+4=5
n+8 = 2+8=10
n+12=3+12=15
n+16=4+16=20
n+20=5+20=25
n+24=6+24=30
n+28=7+28=35
n+32=8+32=40
n+36=9+36=45
n+40=10+40=50