Question

Show that one and only one of n, n + 2 and n + 4 is divisible by 3.​

Answer 1

Step-by-step explanation:

If n=3k, then

n+2=3k+2, therefore remainder is 2.

n+4=3k+4=3(k+1)+1, therefore remainder is 1.

If n+2=3k, then

n=3k-2=3(k-1)+1, therefore remainder is 1.

n+4=3k+2, therefore remainder is 2.

If n+4=3k, then

n=3k-4=3(k-2)+2, therefore remainder is 2.

n+2=3k-2=3(k-1)+1, therefore remainder is 1.

Therefore, only one is divisible by 3. Q.E.D

Answer 2

Answer:

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