Volume 46 | Number 1 | Year 2017 | Article Id. IJMTT-V46P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P510

In number theory Fermat’s last theorem states that no three positive integers a,b,c satisfy the equation an + bn = cn for all exponents including n ≥ 3. This can be proved simply by considering the prime factors associated with one of the members a or b in the equation. It is found that when the exponent is greater than 2 , one or two numbers are invariably either complex or irrational. The non-existence of the relation with all are whole integers proves FLT for all exponents n ≥ 3 .However if the exponents are not same then the three member multi-power relation becomes possible. An unique property associated with these relations is described by Beal conjecture. The Pythagoras theorem, FLT and Beal conjecture are different forms of one and the same multi-power relation under different condition. The inherent linkage between them helps to prove both the Fermat’s last theorem and Beal conjecture in five successive steps.

1.Simon Singh, „Fermat‟s Last Theorem‟ (1997) Fourth Estate Ltd.

2.Jackson,A. „Fermat‟s Enigma „ (1997) Review, AMS.

3.Edward,H.M.,”Fermat‟s Last Theorem – a genetic introduction to the Number Theory‟ (1997),Springer. 4.Wagstaff,S., AMS Notices No.167,(1976)p A-53,244

5.Andrew Wills, „Modular elliptic curve and Fermat‟s last theorem‟ (1995) Annals of Maths., 141, 443-551.

6.Gerd Faltings., “ The proof of Fermat‟s Last Theorem by R.Taylor and A.Wills” AMS,1995,42 (7),743-746.

7. M.Meyyappan http://www.ijmttjournal.org/2017/volume-45number-1/IJMTT-V45P503

8. G.Gadzirayi Nyambuya “ A simple and General Proof of Beal Conjecture, Adv.in Pure.Math, 2014, 4, 518-521

9. R.C.Thiagarajan,” A proof to Beal‟s Conjecture” Bull.Maths.Sci & appl, 2014,89-93

10. L.Torres di Gregorio, “Proof for the Beal conjecture and a new proof for Fermat‟s last theorem” Pure & appl.Math.J, (2013) 2(5),149-155.

M.Meyyappan, "Resolving Fermat‟s Last Theorem by Prime Factor Method and Proof in 5 steps," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 46, no. 1, pp. 50-52, 2017. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V46P510