CHEZ FERMAT A.D. 1637' Erkka Maula and Eero Kasanen Abstract ...

160 ERKKA MAULA & EERO KASANEN
kable'.
Moreover, if FLT fails for odd exponents, (16) and (17) with
the equality signs give rise to second degree equations whose
roots determine when the equilibrium holds. Let the roots be
called (6*,'t*). For (16) the y are (a 2 ± a.r{1/2(b+c)2-a 2 ,2»): (b+c)
and for (17) (1/./2)(a 2 ± r( (b+c)Z-a 2 ,2) ):(b+c).
University of Tampere
NOTES
This essay is dedicated to the memory of our friends Prof.
Hiromichi Takeda - the last Samurai in the fields of philosophy,
and Prof. Tadao Yamada - humanist, scientist, musician. They
were wonderful interpreters of the harmony of Kyoto, of the
song of nature, and of the best aspects of Japan's culture.
* Editor's note: In this article, an option has been taken for a
linear format. Thus the n-th power of x, xn, is written p(x,n) and
the n-th root of x is written r(x,n). x with subscript y is written
x"'y.
REFERENCES
The main biographical source is Mahoney [10] and the best
overview of literature Ribenboim [15], with bibliographies and
primary sources. Fermat's Oeuvres, ed. Tannery & Henry, Paris
(1891) 1922.
[1] Bashmakova, loG. "Diophante et Fermat", Rev. Bist. Sei.
XlX:289-306.
[2] Bashmakova, l.G. & Slavutin, E.I. Istoriya diofantova analiza
Dt Diofanta do Ferma, Moscow, 1984 ("Nauka").
[3] Dickson, L.E. History of the Theory of Numbers II,
Washington, 1920.
[4] Goldziher, K. "Hâtvanyszamok Telbontâsa hâtvanyszamok 08Szegere",
Kozépiskolai Math. Lapok 21:177-184 (1913); his result
was rediscovered in 1952 by Mihaljinec and in 1969 by
Rameswar Rao [15:69].
[5] Grünert, J.A. "Wenn n > 1, so gibt es unter den ganzen
Zahlen von 1 bis n nicht zwei Werte von x und y, für welche,
wenn z einen ganzen Wert bezeichnet, xn+yn = zn ist", Arehiv