Édouard Manet (1832-1883) is considered the 'father' of Impressionism and even of XXth century modern art. Manet's genius involved getting away from the classical narrative or historical topics and replacing them by the banality of daily life. Technically, he erased volumes into flat two-dimensional coloured planes, and distorted conventional perspective with often gross brushstrokes intentiona...

In 1849, Alphonse de Polignac conjectured that every odd positive integer can be written in the form 2n + p, for some integer n ≥ 0 and some prime p. In 1950, Erdős constructed infinitely many counterexamples to Polignac’s conjecture. In this article, we show that there exist infinitely many positive integers that cannot be written in either of the forms Fn + p or Fn− p, where Fn is a Fibonacci...