Mark Haddon currently has an interesting blog, is a writer and illustrator of numerous children’s books and teaches creative writing for the Avron Foundation, living in Oxford, England. He has worked with autistic individuals as a young man.

Christopher Boone, the autistic 15-year-old narrator of this revelatory novel, relaxes by groaning and doing math problems in his head, eats red-but not yellow or brown-foods and screams when he is touched. Strange as he may seem, other people are far more of a conundrum to him, for he lacks the intuitive “theory of mind” by which most of us sense what’s going on in other people’s heads. When his neighbor’s poodle is killed and Christopher is falsely accused of the crime, he decides that he will take a page from Sherlock Holmes (one of his favorite characters) and track down the killer.

Question: Prove the following result: A triangle with sides that can be written in the form n³ + 1, n²-1 and 2n (where n>1) is right angled. Show by means of a counterexample, that the converse is false.