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Dahanayaka, Ekanayake & Piyadasa
2 2
3
In other words,−6ℎ − 4ℎ + Edwards, H.M. 91197). Fermat’s last
1 > 0. This quadratic expression in is theorem, A Genetic Introduction to
positive and does not change the sign and Algebraic Number Theory. Springer -
therefore its discriminant should be Verlag.
2
6
negative. This means 16ℎ + 24ℎ should Manike, K.R.C.J., Ekanayake, E.M.P., &
be negative.This is impossible since ℎ > 0. Piyadasa, R.A.D. (2012). New Set of
By virtue of which we conclude that (3) Primitive Pythagorean Triples and Proofs
never be satisfied with non-zero ℎ. Hence, of Two Fermat’s Theorems. Proceedings of
the proof of FLT for n = 4 follows. the Annual Research Symposium, Faculty
of Graduate Studies, University of
3 CONCLUSION Kelaniya, 113-114.
We have a proved FLT for n = 4 Suzuki, Yasutaka. (1986). Simple Proof of
without using the Method of Infinite Fermat’s Last Theorem for n=4. Proc.
Descent of Fermat and at the same time Japan Acad. 92(A), 209-210
using elementary Mathematics. Therefore, Mitchell, D.W. (2001). An alternative
in order to prove Fermat’s last theorem for characterization of all primitive
all indices we must prove FLT for any odd Pythagorean triples. Mathematical Gazette,
prime [1] using the same technique. We 85(July), 273-275
believe that this can be done easily. Piyadasa, R.A.D. (2011). A simple and
short analytical proof of Fermat’s Last
REFERENCE Theorem. CNMSEM, 2(3).
Ribenboim, P. (1991). Fermat’s last
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