The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and...

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid...

its diagonals Euclid–Euler theorem, characterizing even perfect numbers Euler's theorem, on modular exponentiation Euler's partition theorem relating the...

millennia later, Leonhard Euler proved that all even perfect numbers are of this form. This is known as the Euclid–Euler theorem. It is not known whether...

numbers or not. This is due to the Euclid–Euler theorem, partially proved by Euclid and completed by Leonhard Euler: even numbers are perfect if and only...

antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem asserts a one-to-one correspondence between even perfect numbers...

sum of two primes, in a 1742 letter to Euler. Euler proved Alhazen's conjecture (now the Euclid–Euler theorem) that all even perfect numbers can be constructed...

Pythagorean theorem is equivalent to the fifth. That is, Euclid's fifth postulate implies the Pythagorean theorem and vice-versa. The Pythagorean theorem generalizes...

known as the Euclid–Euler theorem. Euler also conjectured the law of quadratic reciprocity. The concept is regarded as a fundamental theorem within number...

many prime numbers Euclid's lemma, also called Euclid's first theorem, on the prime factors of products The Euclid–Euler theorem characterizing the even...

deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these...

In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers...

second factor zero, or they would not satisfy Fermat's little theorem. This is Euler's criterion. This proof only uses the fact that any congruence k...

Erdős–Rado theorem (set theory) Erdős–Stone theorem (graph theory) Erdős–Szekeres theorem (discrete geometry) Euclid's theorem (number theory) Euclid–Euler theorem...

number is the perfect number 496, of the form 2(5 − 1)(25 − 1) by the Euclid-Euler theorem. 31 is also a primorial prime like its twin prime (29), as well as...

Euclid. Euclidean algorithm Extended Euclidean algorithm Euclidean division Euclid–Euler theorem Euclid number Euclid's lemma Euclid's orchard Euclid–Mullin...

numbers, which had fascinated mathematicians since Euclid. Euler made progress toward the prime number theorem and conjectured the law of quadratic reciprocity...

they appear in Euclid's Elements, Props. IX.32 (on the factorization of powers of two) and IX.36 (half of the Euclid–Euler theorem, on the structure...

They are named after the ancient Greek mathematician Euclid, in connection with Euclid's theorem that there are infinitely many prime numbers. For example...

not able to prove this result; Euler later proved it in the 18th century, and it is now called the Euclid–Euler theorem. Alhazen solved problems involving...

prime n {\displaystyle n} , and is therefore pernicious. By the Euclid–Euler theorem, the even perfect numbers take the form 2 n − 1 ( 2 n − 1 ) {\displaystyle...

defined in Book One of Euclid's Elements. The names used for modern classification are either a direct transliteration of Euclid's Greek or their Latin...

absolutely evident were called postulates or axioms; for example Euclid's postulates. All theorems were proved by using implicitly or explicitly these basic...

still work out to ap − a, as needed.) This proof, due to Euler, uses induction to prove the theorem for all integers a ≥ 0. The base step, that 0p ≡ 0 (mod p)...

recently Christopher gave a partition-theoretic proof. Euler succeeded in proving Fermat's theorem on sums of two squares in 1749, when he was forty-two...

\ } and Dirichlet's theorem states that this sequence contains infinitely many prime numbers. The theorem extends Euclid's theorem that there are infinitely...

close enough. Or, in the (also intrinsic) axiomatic approach analogous to Euclid's axioms of plane geometry, "great circle" is simply an undefined term, together...

Pythagorean theorem using the fact that the altitude bisects the base and partitions the isosceles triangle into two congruent right triangles. The Euler line...

of perfect, abundant and deficient numbers. Euler's rule is a generalization of the Thâbit ibn Qurra theorem. It states that if p = ( 2 n − m + 1 ) × 2...

compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use...