Thre are infinitely many solutions.
The smalest set with two different triangular number adding to another is
6 + 15 = 21
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The sum of the first n cubed numbers is the square of the nth triangular number.
171700
The absolute value of the sum of two complex numbers is less than or equal to the sum of their absolute values.
One relationship is that the sum of the nth and the previous triangular numbers is equal to the nth square number.That isT(n-1) + T(n) = S(n)where T(n) is the nth triangular number and S(n) is the nth square number.
1+3+6+10 =20