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The fundamental theorem of arithmetic dissected

  • Ahmet G. Agargün (a1) and Colin R. Fletcher (a2)

There are hints of unique factorisation in Greek arithmetic. Indeed, some commentators have seen the Fundamental Theorem of Arithmetic (FTA), that the natural numbers can be expressed as products of primes in a unique way, lurking in Euclid’s Elements (c. 300BC). What can be said with certainty is that the history of the FTA is strangely obscure. It is not too much of an exaggeration to say that the result passed from being unknown to being obvious without a proof passing through the head of any mathematician.

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1. Heath, T. L., The thirteen books of Euclid’s Elements, Vol. 2. Cambridge (1908).
2. Agargun, A. G. and Fletcher, Colin R., al-Farisi and the fundamental theorem of arithmetic, Hist. Math. 21 (1994) pp. 162173.
3. Rashed, R., Matériaux pour l’histoire des nombres amiables, J. Hist. Arabic Sei. 6 (1982) pp. 209278.
4. Goldstein, C., On a seventeenth century version of the fundamental theorem of arithmetic, Hist. Math. 19 (1992) pp. 177187.
5. Gauss, C. F., Disquisitiones arithmeticae, Yale University Press (1966).
6. Baker, A., A concise introduction to the theory of numbers, Cambridge (1984).
7. Carmichael, R. D., The theory of numbers. Dover, New York (1959).
8. Dickson, L. E., Introduction to the theory of numbers, Dover, New York (1957).
9. Wright, H. N., First course in theory of numbers, John Wiley, New York (1964).
10. Allenby, R. B. J. T., Rings, fields and groups, Edward Arnold (1991).
11. Davenport, H., The higher arithmetic, Hutchinson House (1952).
12. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers, Oxford (1938).
13. Hunter, I., Number theory, Oliver and Boyd (1964).
14. Shockley, J. E., Introduction to number theory Holt, Rinehart and Winston, New York (1967).
15. Shanks, D., Solved and unsolved problems in number theory, Vol. I, Spartan Books, Washington (1962).
16. Stewart, B. M., Theory of numbers, Macmillan, New York (1952).
17. Jones, B. W., The theory of numbers, Holt, Rinehart and Winston, New York (1955).
18. Stark, H. M., An introduction to number theory, Markham, Chicago (1971).
19. Wright, E. M., Number theory and other reminiscences of Viscount Cherwell, Notes and Records Roy. Soc. London 42 (1988) pp. 197204.
20. Lindemann, F. A., The unique factorization of a positive integer, Quart. J. of Math. 4 (1933) pp. 319320.
21. Niven, I. and Zuckerman, H. S., An introduction to the theory of numbers, John Wiley, New York (1960).
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The Mathematical Gazette
  • ISSN: 0025-5572
  • EISSN: 2056-6328
  • URL: /core/journals/mathematical-gazette
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