Question

prove that one and only one out of N N + 2 or n + 4 is divisible by 3 Where n is any positive integer ​

Answer 1

Answer:

Let n=3q, 3q+1, 3q+2

by EDL

case1: n=3q ______ divisible by 3

n2=3q+2

n4=3q+4

case2: n=3q+1

n2=3q+1+2 _______divisible by 3

n4=3q+1+4

case3: n=3q+2

n=3q+2+2

n=3q+2+4 ________divisible by3

Hence, one of n,n+2andn+4 is divisible by 3