In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n-gonal numbers. That is, every...

a ray of light Fermat polygonal number theorem, about expressing integers as a sum of polygonal numbers Fermat's right triangle theorem, about squares...

Fermat's Last Theorem is a popular science book (1997) by Simon Singh. It tells the story of the search for a proof of Fermat's Last Theorem, first conjectured...

triangular. Centered polygonal number Polyhedral number Fermat polygonal number theorem Tattersall, James J. (2005). Elementary Number Theory in Nine Chapters...

In mathematics, a Fermat number, named after Pierre de Fermat (1607–1665), the first known to have studied them, is a positive integer of the form: F...

known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy...

10 + 10 + 0. This is a special case of the Fermat polygonal number theorem. The largest triangular number of the form 2k − 1 is 4095 (see Ramanujan–Nagell...

fundamental theorem of algebra. In number theory, he made numerous contributions, such as the composition law, the law of quadratic reciprocity and the Fermat polygonal...

theorem (number theory) Euclid's theorem (number theory) Euclid–Euler theorem (number theory) Euler's theorem (number theory) Fermat's Last Theorem (number...

Fermat number Fermat point Fermat–Weber problem Fermat polygonal number theorem Fermat polynomial Fermat primality test Fermat pseudoprime Fermat quintic...

One of his great successes at that time was the proof of Fermat's polygonal number theorem. He quit his engineering job, and received a one-year contract...

study of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem. Later, it became a significant topic for Euler...

\end{aligned}}} This theorem was proven by Joseph Louis Lagrange in 1770. It is a special case of the Fermat polygonal number theorem. From examples given...

now known as Gauss's Eureka theorem and is a special case of what later became known as the Fermat polygonal number theorem. Look up eureka in Wiktionary...

follow the pattern 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. By the Fermat polygonal number theorem, every number is the sum of at most 12 dodecagonal numbers. D n {\displaystyle...

Society. These conjectures are a partial extension of the Fermat polygonal number theorem to three-dimensional figurate numbers, also called polyhedral...

on their limbs. 5 is a Fermat prime, a Mersenne prime exponent, as well as a Fibonacci number. 5 is the first congruent number, as well as the length...

Wooley's survey article from 2002 was comprehensive at the time. Fermat polygonal number theorem, that every positive integer is a sum of at most n of the n-gonal...

of the five known Fermat primes, there are 31 known constructible polygons with an odd number of sides. The next twenty-eight Fermat numbers, F5 through...

four-square theorem, the set of square numbers is an additive basis of order four, and more generally by the Fermat polygonal number theorem the polygonal numbers...

if and only if the odd prime factors of n are distinct Fermat primes. A regular n-sided polygon can be constructed with origami if and only if n = 2 a...

understand but are very difficult to solve. Examples of this are Fermat's Last Theorem, which was proved 358 years after the original formulation, and...

de Fermat stated (without proof) Fermat's little theorem (later proved by Leibniz and Euler). Fermat also investigated the primality of the Fermat numbers...

British flag theorem Bride's Chair – Illustration of the Pythagorean theorem Fermat's Last Theorem Garfield's proof of the Pythagorean theorem Hsuan thu –...

edition of Arithmetica by Bachet gained fame after Pierre de Fermat wrote his famous "Last Theorem" in the margins of his copy. In modern use, Diophantine...

73 is also the smallest factor of the first composite generalized Fermat number in decimal: 10 4 + 1 = 10 , 001 = 73 × 137 {\displaystyle 10^{4}+1=10...

5, using 3 & 4 (34 - 43). 17 is a Fermat prime. 17 is one of six lucky numbers of Euler. Since seventeen is a Fermat prime, regular heptadecagons can be...

represents all positive integers via the 15 and 290 theorems. 15 is the product of distinct Fermat primes, 3 and 5; hence, a regular pentadecagon is constructible...

of two The Fermat primes, prime numbers that are one plus a power of two The products of powers of two and any number of distinct Fermat primes. Thus...

Sierpiński number? Does the converse of Wolstenholme's theorem hold for all natural numbers? Are all Euclid numbers square-free? Are all Fermat numbers square-free...