Robert Tijdeman (born 30 July 1943 in

Oostzaan Oostzaan () is a municipality and a town in the Zaanstreek, Netherlands , Terminology of the Low Countries, informally Holland, is a country in Northwestern Europe, with Caribbean Netherlands, overseas territories in the Caribbean. It is ...

North Holland North Holland (, ) is a Provinces of the Netherlands, province of the Netherlands in the northwestern part of the country. It is located on the North Sea, north of South Holland and Utrecht (province), Utrecht, and west of Friesland and Flevola ...

) is a Dutch mathematician. Specializing in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

, he is best known for his Tijdeman's theorem. He is a professor of mathematics at the

Leiden University Leiden University (abbreviated as ''LEI''; ) is a Public university, public research university in Leiden, Netherlands. Established in 1575 by William the Silent, William, Prince of Orange as a Protestantism, Protestant institution, it holds the d ...

since 1975, and was chairman of the department of mathematics and computer science at Leiden from 1991 to 1993. He was also president of the Dutch Mathematical Society from 1984 to 1986.Curriculum vitae
from Tijdeman's web site, retrieved 2009-08-26. Tijdeman received his PhD in 1969 from the

University of Amsterdam The University of Amsterdam (abbreviated as UvA, ) is a public university, public research university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities, it is the fourth-oldest academic institution in the Netherlan ...

, and received an honorary doctorate from Kossuth Lajos University in 1999. In 1987 he was elected to the

Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences (, KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. In addition to various advisory a ...

Research

, Tijdeman's theorem states that there are at most a finite number of consecutive powers. Stated another way, the set of solutions in integers ''x'', ''y'', ''n'', ''m'' of the exponential diophantine equation :

y^m = x^n + 1,

for exponents ''n'' and ''m'' greater than one, is finite. (This was a significant step towards resolving Catalan’s conjecture, which

Preda Mihăilescu Preda V. Mihăilescu (born 23 May 1955) is a Romanian mathematician, best known for his proof of the 158-year-old Catalan's conjecture. Biography Born in Bucharest,Stewart 2013 he is the brother of Vintilă Mihăilescu. After leaving Romania i ...

accomplished in 2002.) Tijdeman worked closely with T.N. Shorey on various arithmetic problems. He has also worked on algorithms in the area of discrete tomography

Selected publications

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References

External links

Tijdeman's web site at Leiden
1943 births Living people People from Oostzaan 20th-century Dutch mathematicians 21st-century Dutch mathematicians Number theorists Members of the Royal Netherlands Academy of Arts and Sciences Academic staff of Leiden University University of Amsterdam alumni {{Europe-mathematician-stub