SOLUTION: Show that only one of the numbers n, n+2, n+4 is divisible by 3.

Question 254068: Show that only one of the numbers n, n+2, n+4 is divisible by 3.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You didn't say, but the only way this works is if n is an integer. Use the modulo function.

returns the remainder when n is divided by m. For positive integers, the range of the modulo function is

, therefore for

, the range is

.

So there are three possibilities regardless of the value of n:

For each of the three possibilities, there is only one 0 result, hence only one of the numbers is divisible by 3.

If n is a negative integer, the range of

and the result is the same.

John

RELATED QUESTIONS
Show that one and only one out of n, n+2 and n+4 is divisible by 3, where �n� is any... (answered by ewatrrr)

Show that one and only one out of n, n+2 and n+4 is divisible by 3, where �n� is any... (answered by richard1234)

Show that one and only one out of n, n+2, n+4 is divisible by 3, where n is any positive... (answered by ewatrrr)

show that only one out of n, n+2 or n+4 is divisible by 3 where n is positive... (answered by Edwin McCravy)

Prove that one and only one out of n,n+4,n+8,n+12 and n+16 is divisible by 5,where n is... (answered by math_helper)

Show that one out of n,n+3,n+6,n+9 is divisible by n when n is a natural number? (answered by solver91311)

Using math of induction show that 2^n + (-1)^n+1 is divisible by... (answered by math_helper)

show that the number {{{n^(n-1)-1}}} is divisible by {{{(n-1)^2}}} whenever... (answered by Edwin McCravy)

For what integral values of n is the expression 1^n + 2^n + 3^n + 4^n divisible by 5?... (answered by venugopalramana)