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Pramanik, S., Das, D.K. and Pramanik, P. (2023) Products of Odd Numbers or Prime Number Can Generate the Three Members’ Families of Fermat Last Theorem and the Theorem Is Valid for Summation of Squares of More Than Two Natural Numbers. Advances in Pure Mathematics, 13, 635-641.
https://doi.org/10.4236/apm.2023.1310043

has been cited by the following article:

• TITLE: Tree of Fermat-Pramanik Series and Solution of AM +B2 =C2 with Integers Produces a New Series of (C12- B12)=(C22- B22)=(C32- B32)=Others

  AUTHORS: Panchanan Pramanik, Susmita Pramanik, Sabyasachi Sen

  KEYWORDS: Fermat Theorem, Fermat-Pramanik Tree, Solution of AM +B2 =C2, Deductive Series, Generation of Fermat’s Triode, Generation of Fermat Series

  JOURNAL NAME: Advances in Pure Mathematics, Vol.14 No.3, March 21, 2024

  ABSTRACT: The Fermat–Pramanik series are like below: .The mathematical principle has been established by factorization principle. The Fermat-Pramanik tree can be grown. It produces branched Fermat-Pramanik series using same principle making Fermat-Pramanik chain. Branched chain can be propagated at any point of the main chain with indefinite length using factorization principle as follows: Same principle is applicable for integer solutions of AM+B2=C2which produces series of the type . It has been shown that this equation is solvable with N{A, B, C, M}. where , , M=M1+M2 and M1>M2. Subsequently, it has been shown that using M= M1+M2+M3+... The combinations of Ms should be taken so that the values of both the parts (Cn+Bn)and (Cn-Bn) should be even or odd for obtaining Z{B,C}. Hence, it has been shown that the Fermat triple can generate a) Fermat-Pramanik multiplate, b) Fermat-Pramanik Branched multiplate and c) Fermat-Pramanik deductive series. All these formalisms are useful for development of new principle of cryptography.