In number theory, Tijdeman's theorem states that there are at most a finite number of consecutive powers. Stated another way, the set of solutions in integers...

simple zeros. A generalization of Tijdeman's theorem concerning the number of solutions of ym = xn + k (Tijdeman's theorem answers the case k = 1), and Pillai's...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

conjecture Mordell curve Ramanujan–Nagell equation Størmer's theorem Tijdeman's theorem Thaine's theorem Weisstein, Eric W., Catalan's conjecture, MathWorld Mihăilescu...

Thue's theorem (Diophantine equation) Thue–Siegel–Roth theorem (Diophantine approximation) Tijdeman's theorem (Diophantine equations) Tunnell's theorem (number...

Tijdeman (born 30 July 1943 in Oostzaan, North Holland) is a Dutch mathematician. Specializing in number theory, he is best known for his Tijdeman's theorem...

to its large number of consequences in number theory including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem...

amateur mathematician, while investigating generalizations of Fermat's Last Theorem. Since 1997, Beal has offered a monetary prize for a peer-reviewed proof...

Summer Olympics Robert Tijdeman (born 1943 in Oostzaan) a Dutch mathematician, specializing in number theory, wrote Tijdeman's theorem Trijnie Rep (born 1950...

Theodor Schneider independently proved the more general Gelfond–Schneider theorem, which solved the part of Hilbert's seventh problem described below. The...

and c are given integers. The solutions are described by the following theorem: This Diophantine equation has a solution (where x and y are integers)...

{\displaystyle x^{2}+1=y^{n}} has no nontrivial solutions. Results of Shorey and Tijdeman imply that the number of solutions in each case is finite. Bugeaud, Mignotte...

the Skolem–Mahler–Lech theorem on the zeros of a sequence satisfying a linear recurrence with constant coefficients. This theorem states that, if such a...

the two orthogonal projections of a discrete set. In the proof of his theorem, Ryser also described a reconstruction algorithm, the very first reconstruction...

irrational and transcendental. This follows from the Gelfond–Schneider theorem, which establishes ab to be transcendental, given that a is algebraic and...

of the complete bipartite graph, to prove his theorem. He is also known for the Kővári–Sós–Turán theorem bounding the number of edges that can exist in...

Theodor Schneider in 1935. This result is known as Gelfond's theorem or the Gelfond–Schneider theorem. (The restriction to irrational b is important, since it...

MR 1863009. Shorey and Tijdeman (1986), Theorem 6.1 Shorey and Tijdeman (1986), Theorem 10.2 Shorey and Tijdeman (1986), Theorems 10.6 and 10.7, see also...

Pythagorean quadruple Sums of powers, a list of related conjectures and theorems Discrete tomography Borwein 2002, p. 85. Solution found by Nuutti Kuosa...

finitely many solutions. But this proof depends on Siegel's finiteness theorem, which is ineffective. Nesterenko & Shorey (1998) showed that, if m − 1...

even perfect numbers are of this form. This is known as the Euclid–Euler theorem. It is not known whether there are any odd perfect numbers, nor whether...

term-wise multiplication, and Cauchy product. The Skolem–Mahler–Lech theorem states that the zeros of a constant-recursive sequence have a regularly...

mathematician, Breusch was known for his new proof of the prime number theorem and for the many solutions he provided to problems posed in the American...

(PDF) on 2016-04-19. Retrieved 2015-02-28. Robin Whitty. Lieb's Square Ice Theorem (PDF). Ivan Niven. Averages of exponents in factoring integers (PDF). Steven...

integers, find a subset whose product is a square. By the fundamental theorem of arithmetic, any positive integer can be written uniquely as a product...

he obtained, with Alan Baker, an effective improvement to Liouville's Theorem. In 1991 he proved that the number of solutions to a Thue equation f (...

Indag. Math., 82 (1): 83–86, doi:10.1016/1385-7258(79)90012-X Petersen's theorem Voorhoeve, Marc (1976), "On the oscillation of exponential polynomials"...