In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.

The oxidation of one of these compounds with a Jones reagent yields carboxylic acid, and they are the product of the reaction of a ketone with a Grignard reagent. Esters are formed via a reaction of carboxylic acid and this compound in a process named for Fischer. Consisting of a hydroxyl group bonded to a carbon atom, they are given the formula R-OH. For 10 points, name this class of compounds exemplified by methanol and ethanol, the latter of which is found in hand sanitizer and beer.
Science

Paulo Ribenboim proved in 1991 that the set of these is Diophantine, and in 1912 Edmund Landau proposed four "unattackable problems" dealing with them, none of which have yet been solved. The theorem named for them states that the number of them less than or equal to n is approximately equal to n divided by the natural logarithm of n. The GIMPS project seeks to find examples of the Mersenne type of this number, ordinary examples of which can be found using the sieve of Eratosthenes. For 10 points, identify these numbers whose only two factors are 1 and itself.
Social Science

Galois theory can be applied to the symmetric type of these expressions, which also appear in Vieta's formulas. Weierstrass's theorem uses these to achieve a uniform approximation, and Cardano's theorem is used to solve a specific type of them. There are no general solutions to these expressions with degree (*) five or higher, and they can be simplified using synthetic division. Functions of this type are all continuous and differentiable, and they have at least one complex root according to the fundamental theorem of algebra. For ten points, identify these algebraic expressions that contain variables raised to a power, such as 2y and 3x plus 1.

Science

