Question

Prove that one and only one out of n, n + 2 and n + 4 is divisible by 3, where n is any positive integer

NCERT Class X
Mathematics - Exemplar Problems

Chapter _Real Numbers

Answer 1

Difference between n and n+2 = 2 and n+2 and n+4 = 2 Therefore, if n is divisible by 3, then sum of digits of n = 3x, where x is an integer. Then, n+2 and n+4 not divisible because they add upto 3x +2, 3x +4