the question: (im presuming n^2 means n squared) prove the following result: "a traingle with sides that can be written in the form n^2+1, n^2-1, and 2n (where n>1) is right angled. show, by means of a counter example, that the converse is false. this q was taken from the back of the book "the curious incedent of the dog in the night-time" and there was a full proof but i dont understand some of it. it start by exmplaining we need to prove which side is the longest by doing: n^2+1 - 2n = (n-1)^2 if n>1 then (n-1)^2 >0 therefore n^2+1 > 2n similarily (n^2+1) - (n^2-1) = 2 therefore n^2+1 > n^2-1 so n^2+1 > n^2-1. the rest is worked out using pythagoras but then the converse bit has completly lost me. if anyone would like to explain, then i would be very grateful. thanks!