The Markoff conjecture states that given a positive integer c, there is at most one triple (a, b, c) of positive integers with a ≤ b ≤ c that satisfies the equation a2 + b2 + c2 = 3abc. The conjecture is known to be true when c is a prime power or two times a prime power. We present an elementary proof of this result. We also show that if in the class group of forms of discriminant d = 9c2 − 4,...

Epistemologists take themselves to disagree about whether there are situations where it is rational for one believe that p and one’s evidence does not support (rational akrasia). The embedded sentence ‘one’s p’ can be interpreted in two ways, however, depending on what the semantic contribution of evidence’ taken be. ‘One’s might seen as a sheer indexical or descriptive singular term. first int...