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Robert 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. He is a professor of mathematics at the Leiden University 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.

Tijdeman received his PhD in 1969 from the University of Amsterdam, 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.

Research

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 x, y, n, m of the exponential diophantine equation

${\displaystyle y^{m}=x^{n}+1,}$

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

• Shorey, T. N.; Tijdeman, R. (1990). "On the greatest prime factor of an arithmetical progression". In Baker, A.; Bollobas, B.; Hajnal, A. (eds.). A Tribute to Paul Erdős. Cambridge: Cambridge University Press. pp. 385–390. doi:10.1017/cbo9780511983917.032. ISBN 978-0-511-98391-7.
• Shorey, T.; Tijdeman, R. (11 August 2010). "On the greatest prime factor of an arithmetical progression. II". Acta Arithmetica. 53 (5): 499–504. doi:10.4064/aa-53-5-499-504. ISSN 0065-1036. Retrieved 27 October 2024.
• Shorey, T.N.; Tijdeman, R. (1992). "On the greatest prime factor of an arithmetical progression III". In Philippon, Patrice (ed.). Approximations diophantiennes et nombres transcendants: comptes-rendus du colloque tenu au C.I.R.M de Luminy 18-22 juin 1990. Berlin ; New York: W. de Gruyter. ISBN 978-3-11-013486-5.
• Shorey, T.N.; Tijdeman, R. (1986). Exponential Diophantine Equations. Cambridge, England: Cambridge University Press. ISBN 978-0521268264. OCLC 13010635.

References

1. ^ Curriculum vitae from Tijdeman's web site, retrieved 2009-08-26.
2. Robert Tijdeman at the Mathematics Genealogy Project
3. "Rob Tijdeman" (in Dutch). Royal Netherlands Academy of Arts and Sciences. Retrieved 15 July 2015.
4. Tijdeman, Robert (1976), "On the equation of Catalan", Acta Arithmetica, 29 (2): 197–209, doi:10.4064/aa-29-2-197-209, Zbl 0286.10013
5. Narkiewicz, Wladyslaw (2011), Rational Number Theory in the 20th Century: From PNT to FLT, Springer Monographs in Mathematics, Springer-Verlag, p. 352, ISBN 978-0-857-29531-6
6. Schmidt, Wolfgang M. (1996), Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics, vol. 1467 (2nd ed.), Springer-Verlag, p. 207, ISBN 978-3-540-54058-8, Zbl 0754.11020

External links

• Tijdeman's web site at Leiden.

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