Exeter alumnus Richard Booth (1971, Mathematics) publishes number-theory paper in INTEGERS

Exeter alumnus Richard Booth (1971, Mathematics) has co-authored a new mathematical paper titled “Matched Column Sets in Repetend Tables”, now published in INTEGERS (Volume 25, A26, 2025). Written with D. J. Horton, the paper explores intriguing regularities in repetend tables—grids formed from recurring digit sequences in fractional expansions. 

The publication has now been reviewed by the American Mathematical Society and included in MathSciNet (MR4885376), its leading database of mathematical reviews. 

The research examines how digits align across columns in repetend tables when fractions of the form 1/n are expressed in various number bases. Booth and Horton prove that, for a fixed repetend length (L), these columns contain identical multisets of digits except in a small number of exceptional cases. These “Class A” matches are then extended by identifying further infinite families of “Class B and C” exceptions, all of which demonstrate previously undocumented symmetry and structure in these numerical patterns. 

Their work deepens our understanding of rational number expansions and introduces new combinatorial insights into digit repetition and symmetry. As such, the paper contributes meaningfully to elementary number theory, particularly in the context of periodicity and modular arithmetic. 

As Dr. Booth noted, the paper contains an “uncanny link” to Exeter College, which was founded in 1314. “This appears in Example 8,” he explains, “where 1314 and 10 are two of the 20 bases which have repetend length 25 under the modulus 21401. Row 19 of Table 5 exhibits the actual repetend sequence for base 1314.” Dr. Booth remarked that he was “astonished to see this” when he first generated the example. 

Exeter College congratulates Dr. Booth on this significant publication and review. Readers can access the full paper online via the INTEGERS journal.