Trithagorean Triples
Mathematica, 53 49 48 bytes

Solve[{x.(x+1)==#^2+#,a&gt;=b&gt;0},x={a,b},Integers]&amp;


Example:

In[1]:= Solve[{x.(x+1)==#^2+#,a&gt;=b&gt;0},x={a,b},Integers]&amp;[21]

Out[1]= {{a -&gt; 17, b -&gt; 12}, {a -&gt; 20, b -&gt; 6}}