O, you do mean triangle equality? What are you talking about?values of a,b,c are included in the binomial theorem for case n = 2 that do NOT satisfy the triangle equality.
You're just confused.That covers them all for a and b on disjoint number lines (vectors).
6,3,3 doesn't satisfy the triangle inequality, 6,4,2 doesn't satisfy the triangle inequality, 6,5,1 doesn't satisfy the triangle inequalityc = (a+b) = d on the same number line are simply different names for the same integer.
(the same integer is just partitioned in the case a + b, but there are still just as many elements.)
Let a = 6
That's why one uses vectors.
For n>2, your proof ignores all numbers that satisfy the triangle inequality.
(You really are very slow.... you keep repeating the same dumb objections. Find something more useful to do.... )