1 thought on “Show that one and only one out of n, (n+1) and (n+2) is divisible by 3,where nis<br />any positive integer.<br /><br />”
[tex]\bold\red{\fbox{\sf{Solution}}}[/tex]
Since n, n+1, n+2 are three consecutive integers then there must be one number divisible by 3 at least.
If the remainder at dividing n by 3 is 1, then n+2 must be divisible by 3 and if the remainder at dividing n by 3 is 2, then n+1 must be divisible by 3. Similarly for n+1 and n+2.
Let n be divisible by 3.
3n+1=3n+31
Now, n is divisible by 3 but 1 is not. So we get n+1 not divisible by 3. Similarly,n+2 will not be divisible by 3 as well if n is divisible by 3.
3n+2=3n+32
In the same way, if n+1 is divisible by 3 then n and n+2 can’t be divisible by 3. If n+2 is divisible by 3 then n and n+1 cannot be divisible by 3.
[tex]\bold\red{\fbox{\sf{Solution}}}[/tex]
3n+1=3n+31
3n+2=3n+32