| 释义 |
- Notes
- References
The first case of Fermat's last theorem says that for three integers x, y and z and a prime number p, where p does not divide the product xyz, there are no solutions to the equation xp + yp + zp = 0. Using the Theorem of unique factorization of ideals in Q(ξ) it was shown that if the first case has solutions x, y, z, then x+y+z is divisible by p and (x, y), (y, z) and (z, x) are elements of Hp, where Hp denotes a set of pairs of integers with special properties.[1] Notes1. ^{{Citation | first1=A. | last1=Granville | first2=M. B. | last2=Monagan | title=The First Case of Fermat's Last Theorem is true for all prime exponents up to 714,591,416,091,389 | journal=Transactions of the American Mathematical Society | volume=306 | issue=1 | year=1988 | pages=329–359 | doi=10.1090/S0002-9947-1988-0927694-5 | postscript=.}}
References- {{Citation | last=Coppersmith | first=D. | authorlink=Don Coppersmith | title=Fermat's Last Theorem (Case I) and the Wieferich Criterion | journal=Math. Comp. | volume=54 | issue=190 | pages=895–902 | publisher=AMS | year=1990 | jstor=2008518 |url=http://www.ams.org/journals/mcom/1990-54-190/S0025-5718-1990-1010598-2/S0025-5718-1990-1010598-2.pdf | postscript=. | doi=10.1090/s0025-5718-1990-1010598-2}}
- {{Citation | last=Cikánek | first=P. | title=A Special Extension of Wieferich's Criterion | journal=Math. Comp. | volume=62 | issue=206 | pages=923–930 | jstor=3562296 | publisher=AMS | year=1994 | url=http://www.ams.org/journals/mcom/1994-62-206/S0025-5718-1994-1216257-9/S0025-5718-1994-1216257-9.pdf | postscript=. | doi=10.2307/2153550}}
- {{Citation | last1=Dilcher | first1=K. | last2=Skula | first2=L. | title=A new criterion for the first case of Fermat's last theorem | journal=Math. Comp. | volume=64 | issue=209 | pages=363–392 | jstor=2153341 | publisher=AMS | year=1995 | doi=10.1090/s0025-5718-1995-1248969-6}}
- {{Citation | last1=Lehmer | first1=D. H. | last2=Lehmer | first2=E. | title=On the first case of Fermat's last theorem | journal=Bull. Amer. Math. Soc. | volume=47 | issue=2 | pages=139–142 | year=1941 | url=http://projecteuclid.org/euclid.bams/1183503473 | doi=10.1090/s0002-9904-1941-07393-3}}
- {{Citation | last=Rosser | first=B. | title=On the first case of Fermat's last theorem | journal=Bull. Amer. Math. Soc. | volume=45 | issue=8 | pages=636–640 | year=1939 | url=http://projecteuclid.org/euclid.bams/1183502014 | doi=10.1090/s0002-9904-1939-07058-4}}
- {{Citation | last=Jha | first=V. | title=On Krasnér's theorem for the first case of Fermat's last theorem | journal=Colloqium Mathematicum | volume=67 | pages=25–31 | year=1994 | url=http://matwbn.icm.edu.pl/ksiazki/cm/cm67/cm6714.pdf}}
1 : Fermat's Last Theorem |