Opportunity of inductive proof for Fermat Last Theorem (FLT on an+bn=cn, 1637) is considered and commented starting from the cases n=3-4 proved centuries ago focusing on the systematic generation and count of cardinality of triples which may show promising way to simpler and shorter proof (beside the existing very lengthy one with modular forms 1995). After the brief review of historical milestones, many simple relations are summarized yielding strong sieve together toward FLT. The divisibility vs. co-prime property in Fermat equation is analyzed in relation to exclusion, and the effect of simultaneous values of gcd(a,b,c), gcd(a+b,cn), gcd(c-a,bn) and gcd(c-b,an) on the decrease of cardinality is exhibited.
Topics
Review
REFERENCES
1.
3.
A.
Wiles
: Annals of Mathematics
, 141
(3
), 443
–551
(1995
)4.
S.
Kristyan
: Am. Inst. Phys. Conf. Proc., ICNAAM 2016
, 1863
, 560013
-1
- 560013-4 (2017
)5.
Y.
Hellegouarch
: Polska Akademia Nauk. Instytut Matematyczny. Acta Arithmetica
, 26
(3
), 253
–263
(1974
)6.
7.
8.
K.
Ribet
: Annales de la faculté des sciences de Toulouse Sér
. 5
, 11 (1
), 116
–139
(1990
)9.
Y.
Manin
: Rational points on algebraic curves, Russian Mathematical Surveys
, 19
(6
), 75
–78
(1964
)10.
J. H.
Silverman
: Advanced Topics in the Arithmetic of Elliptic Curves
, Springer-Verlag
, 2009
11.
G.
Faltings
: Inventiones Mathematicae
, 73
(3
), 349
–366
(1983
) with erratum 75 (2), 381 (1984)12.
C.
Sandor
: On the Equation a3+b3+c3=d3
, Periodica Mathematica Hungarica
, 33
(2
), 121
–134
(1996
)13.
L. E.
Dickson
: History of the Theory of Numbers, Volume 2.
, New York, Chelsea
, 1952
14.
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