Granville, A;
(2017)
Squares in Arithmetic Progressions and Infinitely Many Primes.
The American Mathematical Monthly
, 124
(10)
pp. 951-954.
10.4169/amer.math.monthly.124.10.951.
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Abstract
We give a new proof that there are infinitely many primes, relying on van der Waerden's theorem for coloring the integers, and Fermat's theorem that there cannot be four squares in an arithmetic progression. We go on to discuss where else these ideas have come together in the past.
| Type: | Article |
|---|---|
| Title: | Squares in Arithmetic Progressions and Infinitely Many Primes |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4169/amer.math.monthly.124.10.951 |
| Publisher version: | http://dx.doi.org/10.4169/amer.math.monthly.124.10... |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Integers, Arithmetic progressions, Mathematical theorems, Fermats theorem, Arithmetic, Rational numbers, Squares, Geometry, Combinatorics, math.NT, 11N05 (Primary), 11A41, 11B25 (Secondary) |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1572097 |
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