Claude Gaspard Bachet (sieur de Méziriac). Problèmes plaisants & délectables qui se font par les nombres, 2nd, Lyons, France: Pierre Rigaud & Associates, 18–33. o. (1624) On these pages, Bachet proves (without equations) “Proposition XVIII. Deux nombres premiers entre eux estant donnez, treuver le moindre multiple de chascun d’iceux, surpassant de l’unité un multiple de l’autre.” (Given two numbers [which are] relatively prime, find the lowest multiple of each of them [such that] one multiple exceeds the other by unity (1).) This problem (namely, ax - by = 1) is a special case of Bézout’s equation and was used by Bachet to solve the problems appearing on pages 199 ff.
