that implies both the six exponentials theorem and the five exponentials theorem is the sharp six exponentials theorem. This theorem is as follows. Let x1...

is a "perfect ruler". The six exponentials theorem guarantees that under certain conditions one of a set of six exponentials is transcendental. The smallest...

of four exponentials. The conjecture, along with two related, stronger conjectures, is at the top of a hierarchy of conjectures and theorems concerning...

Gelfond–Schneider theorem. It is not quite as encompassing as the still unproven Schanuel's conjecture, and does not imply the six exponentials theorem nor, clearly...

that e is transcendental Q-exponential Radioactive decay Rule of 70, Rule of 72 Scientific notation Six exponentials theorem Spontaneous emission Super-exponentiation...

theory) Siegel–Walfisz theorem (analytic number theory) Six exponentials theorem (transcendental number theory) Skolem–Mahler–Lech theorem (number theory) Solutions...

primes, which Siegel assured them was true—a special case of the six exponentials theorem proven in the 1960s by Serge Lang and K. Ramachandra —they managed...

Chapter 1, Theorem 1.4, is the following: An equivalent formulation—If α1, ..., αn are distinct algebraic numbers, then the exponentials eα1, ..., eαn...

then t {\displaystyle t} itself must be an integer. The related six exponentials theorem has been proven. Schanuel's conjecture, if proved, would also establish...

Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Mermin–Wagner–Coleman theorem) states that continuous...

transcendental number theory, in which he is known for his proof of the six exponentials theorem, achieved independently of Serge Lang. He also contributed to many...

The infinite monkey theorem states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will...

In computational complexity theory, the linear speedup theorem for Turing machines states that given any real c > 0 and any k-tape Turing machine solving...

article on Ramsey's theorem for a rigorous proof. Another way to express this result is as follows: at any party with at least six people, there are three...

characterization of the exponential function was discovered by Leonhard Euler. The six most common definitions of the exponential function exp ⁡ ( x ) =...

In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete...

than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself...

differentiable. ATS theorem Carleson's theorem Dirichlet kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier...

not depend on their parameters, the Pitman–Koopman–Darmois theorem states that only exponential families have sufficient statistics of dimensions that are...

{(\cos \theta )}^{2}.} This can be viewed as a version of the Pythagorean theorem, and follows from the equation x 2 + y 2 = 1 {\displaystyle x^{2}+y^{2}=1}...

in finding these patterns in Conway's Game of Life. The Garden of Eden theorem of Moore and Myhill asserts that a cellular automaton on the square grid...

Conjecturing) in 1713. He named this his "golden theorem" but it became generally known as "Bernoulli's theorem". This should not be confused with Bernoulli's...

four color theorem is that every snark is a non-planar graph. Research on snarks originated in Peter G. Tait's work on the four color theorem in 1880, but...

describing such behaviour are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential...

implicit function theorem, and many authors have attempted to put the logic of the proof into the setting of a general theorem. Such theorems are now known...

all trigonometric functions in terms of complex exponentials and using properties of the exponential function. The cosine and the secant are even functions;...

triangle (مثلث خیام) in Iran. Several theorems related to the triangle were known, including the binomial theorem. Khayyam used a method of finding nth...

forms a K 3 , 3 {\displaystyle K_{3,3}} subgraph. The Kővári–Sós–Turán theorem provides an upper bound on the solution to the Zarankiewicz problem. It...

a die, where a six is "success" and everything else a "failure". In this case, there are six possible outcomes, and the event is a six; the complementary...

Chebyshev's theorem (Hardy & Wright 1979, thm.7) and Mertens' third theorem is all that is needed. Hardy & Wright 1979, thm. 436 Theorem 15 of Rosser...