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The fundamental theorem of arithmetic dissected

Published online by Cambridge University Press:  01 August 2016

Ahmet G. Agargün and
Colin R. Fletcher
Ahmet G. Agargün
Affiliation:
Yildiz Teknik Üniversitesi, Istanbul, Turkey
Colin R. Fletcher
Affiliation:
Department of Mathematics, University of Wales, Aberystwyth SY23 3BZ
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Extract

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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Articles
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The Mathematical Gazette , Volume 81 , Issue 490 , March 1997, pp. 53 - 57
Copyright
Copyright © The Mathematical Association 1997

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References

1. Heath, T. L., The thirteen books of Euclid’s Elements, Vol. 2. Cambridge (1908).Google Scholar
2. Agargun, A. G. and Fletcher, Colin R., al-Farisi and the fundamental theorem of arithmetic, Hist. Math. 21 (1994) pp. 162–173.Google Scholar
3. Rashed, R., Matériaux pour l’histoire des nombres amiables, J. Hist. Arabic Sei. 6 (1982) pp. 209–278.Google Scholar
4. Goldstein, C., On a seventeenth century version of the fundamental theorem of arithmetic, Hist. Math. 19 (1992) pp. 177–187.Google Scholar
5. Gauss, C. F., Disquisitiones arithmeticae, Yale University Press (1966).Google Scholar
6. Baker, A., A concise introduction to the theory of numbers, Cambridge (1984).Google Scholar
7. Carmichael, R. D., The theory of numbers. Dover, New York (1959).Google Scholar
8. Dickson, L. E., Introduction to the theory of numbers, Dover, New York (1957).Google Scholar
9. Wright, H. N., First course in theory of numbers, John Wiley, New York (1964).Google Scholar
10. Allenby, R. B. J. T., Rings, fields and groups, Edward Arnold (1991).Google Scholar
11. Davenport, H., The higher arithmetic, Hutchinson House (1952).Google Scholar
12. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers, Oxford (1938).Google Scholar
13. Hunter, I., Number theory, Oliver and Boyd (1964).Google Scholar
14. Shockley, J. E., Introduction to number theory Holt, Rinehart and Winston, New York (1967).Google Scholar
15. Shanks, D., Solved and unsolved problems in number theory, Vol. I, Spartan Books, Washington (1962).Google Scholar
16. Stewart, B. M., Theory of numbers, Macmillan, New York (1952).Google Scholar
17. Jones, B. W., The theory of numbers, Holt, Rinehart and Winston, New York (1955).Google Scholar
18. Stark, H. M., An introduction to number theory, Markham, Chicago (1971).Google Scholar
19. Wright, E. M., Number theory and other reminiscences of Viscount Cherwell, Notes and Records Roy. Soc. London 42 (1988) pp. 197–204.Google Scholar
20. Lindemann, F. A., The unique factorization of a positive integer, Quart. J. of Math. 4 (1933) pp. 319–320.CrossRefGoogle Scholar
21. Niven, I. and Zuckerman, H. S., An introduction to the theory of numbers, John Wiley, New York (1960).Google Scholar