Question: What nationality was the mathematician who proposed the Legendre's conjecture?

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Cristian Dumitru Popescu: Cristian Dumitru Popescu is a Romanian-American mathematician at the University of California, San Diego.  His research interests are in Algebraic Number Theory, and in particular, in special values of L-functions.  He formulated and proved function-field versions of the Gras conjectures and Rubin's integral refinement of the abelian Stark conjectures.  He has also made important contributions to the Stark conjectures over number fields, formulating an alternative to Rubin's refinement, known as Popescu's conjecture.  Although slightly weaker than Rubin's conjecture, it has the advantage that it can presently be shown to remain true under raising the base field or lowering the top field of the extension.  Recently, Popescu and Cornelius Greither have formulated equivariant versions of Iwasawa's main conjecture over function fields and global fields, proving most the version for function fields.  These conjectures have important implications for the Brumer–Stark conjecture and Gross' conjecture on special values of L-functions.

Mehdi Behzad: Mehdi Behzad (Persian:مهدی بهزاد; born April 22, 1936) is a mathematician of Iranian origin specializing in graph theory.  He introduced his total coloring theory (also known as "Behzad's conjecture" or "the total chromatic number conjecture") during his Ph.D. studies in 1965.  Despite the active work during the last 50 years this conjecture remains as challenging as it is open.  In fact, Behzad's conjecture now belongs to mathematics’ classic open problems.

Legendre transform: In mathematics, Legendre transform is an integral transform named after the mathematician Adrien-Marie Legendre, which uses Legendre polynomials formula_1 as kernels of the transform.  Legendre transform is a special case of Jacobi transform.

Carlitz–Wan conjecture: In the field of mathematics, the Carlitz–Wan conjecture classifies the possible degrees of exceptional polynomials over a finite field "F" of "q" elements.  Recall that a polynomial "f"("x") in "F"["x"] of degree "d" is called exceptional over "F" if every irreducible factor (differing from "x" − "y") of ("f"("x") − "f"("y"))/("x" − "y") over "F" will become reducible over the algebraic closure of "F".  If "q" > "d", then "f"("x") is exceptional if and only if "f"("x") is a permutation polynomial over "F".  The Carlitz–Wan conjecture states that there are no exceptional polynomials of degree "d" over "F" if ("d", "q" − 1) >  1.  In the special case that "q" is odd and "d" is even, this conjecture was proposed by Carlitz (1966) and proved by Fried–Guralnick–Saxl (1993) The general form of the Carlitz–Wan conjecture was proposed by Daqing Wan (1993)

Abc conjecture: The "abc" conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory, first proposed by and .  It is stated in terms of three positive integers, "a", "b" and "c" (hence the name) that are relatively prime and satisfy "a" + "b" = "c".  If "d" denotes the product of the distinct prime factors of "abc", the conjecture essentially states that "d" is usually not much smaller than "c".  In other words: if "a" and "b" are composed from large powers of primes, then "c" is usually not divisible by large powers of primes.  The precise statement is given below.

Vaught conjecture: The Vaught conjecture is a conjecture in the mathematical field of model theory originally proposed by Robert Lawson Vaught in 1961.  It states that the number of countable models of a first-order complete theory in a countable language is finite or ℵ or 2 .  Morley showed that number of countable models is finite or ℵ or ℵ or 2 , which solves the conjecture except for the case of ℵ models when the continuum hypothesis fails.  For this remaining case, has announced a counterexample to the Vaught conjecture and the topological Vaught conjecture.  As of 2016 the counterexample has not been verified.

Hodge conjecture: In mathematics, the Hodge conjecture is a major unsolved problem in the field of algebraic geometry that relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of that variety.  More specifically, the conjecture says that certain de Rham cohomology classes are algebraic, that is, they are sums of Poincaré duals of the homology classes of subvarieties.  It was formulated by the Scottish mathematician William Vallance Douglas Hodge as a result of a work in between 1930 and 1940 to enrich the description of de Rham cohomology to include extra structure that is present in the case of complex algebraic varieties.  It received little attention before Hodge presented it in an address during the 1950 International Congress of Mathematicians, held in Cambridge, Massachusetts, U.S.  The Hodge conjecture is one of the Clay Mathematics Institute's Millennium Prize Problems, with a prize of $1,000,000 for whoever can prove or disprove the Hodge conjecture.

Adrien-Marie Legendre: Adrien-Marie Legendre (] ; 18 September 1752 – 10 January 1833) was a French mathematician.  Legendre made numerous contributions to mathematics.  Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him.

Legendre's conjecture: Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between "n" and ("n" + 1) for every positive integer "n".  The conjecture is one of Landau's problems (1912) on prime numbers; as of 2017 , the conjecture has neither been proved nor disproved.

Oppermann's conjecture: Oppermann's conjecture is an unsolved problem in mathematics on the distribution of prime numbers.  It is closely related to but stronger than Legendre's conjecture, Andrica's conjecture, and Brocard's conjecture.  It is named after Danish mathematician Ludvig Oppermann, who posed it in 1882.

Supporting paragraphs: Legendre's conjecture Adrien-Marie Legendre
Answer: French