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Number theory is a vast area of mathematics with several different flavours. Core questions that are dealt with in analytic-number-theory are approximating the density of prime-numbers (be it in all or in some residue class modulo a prime) and studying the riemann-zeta-function or more general L-functions. In algebraic number theory, behaviour of ideals under extensions and contractions is one of the central problems. The subject diophantine-equations is the study of integer solutions to certain, mostly polynomial, equations such as Pell's equation. Transcendental number theory is one other challenging, subject which starts from transcendence of $e$, $\pi$.

A very popular subject of study, the field of number theory is rich in open problems, such as the riemann-hypothesis, the Ramanaujan conjecture, the Goldbach conjecture, and the (non-)existence of odd perfect numbers.

Number theory is a vast area of mathematics with several different flavours. Core questions that are dealt with in analytic-number-theory are approximating the density of prime-numbers (be it in all or in some residue class modulo a prime) and studying the riemann-zeta-function or more general L-functions. In algebraic number theory, behaviour of ideals under extensions and contractions is one of the central problems. The subject diophantine-equations is the study of integer solutions to certain, mostly polynomial, equations such as Pell's equation. Transcendental number theory is one other challenging subject which starts from transcendence of $e$, $\pi$.

A very popular subject of study, the field of number theory is rich in open problems, such as the riemann-hypothesis, the Ramanujan conjecture, the Goldbach conjecture, and the (non-)existence of odd perfect numbers.

Number theory is a vast area of mathematics with several different flavours. Core questions that are dealt with in analytic-number-theory are approximating the density of prime-numbers (be it in all or in some residue class modulo a prime) and studying the riemann-zeta-function. In algebraic number theory, behaviour of ideals under extensions and contractions is one of the central problems. The subject diophantine-equations is the study of integer solutions to certain, mostly polynomial, equations such as Pell's equation. Transcendental number theory is one other challenging, subject which starts from transcendence of $e$, $\pi$.

A very popular subject of study, the field of number theory is rich in open problems, such as the riemann-hypothesis, the Ramanaujan conjecture, the Goldbach conjecture, and the (non)existence of odd perfect numbers.

Number theory is a vast area of mathematics with several different flavours. Core questions that are dealt with in analytic-number-theory are approximating the density of prime-numbers (be it in all or in some residue class modulo a prime) and studying the riemann-zeta-function or more general L-functions. In algebraic number theory, behaviour of ideals under extensions and contractions is one of the central problems. The subject diophantine-equations is the study of integer solutions to certain, mostly polynomial, equations such as Pell's equation. Transcendental number theory is one other challenging, subject which starts from transcendence of $e$, $\pi$.

A very popular subject of study, the field of number theory is rich in open problems, such as the riemann-hypothesis, the Ramanaujan conjecture, the Goldbach conjecture, and the (non-)existence of odd perfect numbers.

Number theory is a vast area of mathematics with several different flavours. Core questions that are dealt with in analytic number theory are approximating the density of prime numbers (be it in all or in some residue class modulo a prime) and studying the Riemann zeta function. In algebraic number theory, behaviour of ideals under extensions and contractions is one of the central problems. Diophantine equations study integer solutions to certain polynomial equations such as Pell's equation. Transcendental number theory is one other challenging, subject which starts from transcendence of $e$, $\pi$.

A very popular subject of study, the field of number theory is rich in open problems, such as the Riemann hypothesis, the Ramanaujan conjecture, the Goldbach conjecture, and the (non)existence of odd perfect numbers.

Number theory is a vast area of mathematics with several different flavours. Core questions that are dealt with in analytic-number-theory are approximating the density of prime-numbers (be it in all or in some residue class modulo a prime) and studying the riemann-zeta-function. In algebraic number theory, behaviour of ideals under extensions and contractions is one of the central problems. The subject diophantine-equations is the study of integer solutions to certain, mostly polynomial, equations such as Pell's equation. Transcendental number theory is one other challenging, subject which starts from transcendence of $e$, $\pi$.

A very popular subject of study, the field of number theory is rich in open problems, such as the riemann-hypothesis, the Ramanaujan conjecture, the Goldbach conjecture, and the (non)existence of odd perfect numbers.