The whole paper is a proof with the displayed equations representing the key points and solutions. The ‘remarks’ that seem to annoy you are merely the author adjectives to qualify the underlying approach, and to avoid the trivial (for the author) intermediate steps. I highly doubt that you and your ‘friends’ are going to find a single mathematical mistake in this humoristic paper (the actual work of the author being quite full of your standard Lemma/Theorem/Proof sectioning without which you seem to be lost).