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Can you explain (1) ? I am trying to solve the equation but I am not so sure it's the right method.

If x+y is divisible by 3 => x+y = 3n , when n = integer -(a) If x-y is divisible by 3 => x-y = 3m, when m = integer -(b)

From (a) and (b) => x = 3(m+n)/2 and y = 3(n-m)/2

Just extend your analysis further...

Since x and y are integers then (m+n)/2 and (m-n)/2 have to either integers
or k/3.
For no integers pairs (m,n) (m+n)/2 or (m-n)/2 yields k/3 Hence
(m+n)/2 and (m-n)/2 have to be integers. If they are integers then both x and y are divisible by 3

Can you explain (1) ? I am trying to solve the equation but I am not so sure it's the right method.

If x+y is divisible by 3 => x+y = 3n , when n = integer -(a) If x-y is divisible by 3 => x-y = 3m, when m = integer -(b)

From (a) and (b) => x = 3(m+n)/2 and y = 3(n-m)/2

Just extend your analysis further...

Since x and y are integers then (m+n)/2 and (m-n)/2 have to either integers or k/3. For no integers pairs (m,n) (m+n)/2 or (m-n)/2 yields k/3 Hence (m+n)/2 and (m-n)/2 have to be integers. If they are integers then both x and y are divisible by 3

Got a technical question here,
is 0 divisible by 3?