# Joachim Moussounda MouandaBlessington Christian University · Mathematics

Joachim Moussounda Mouanda

Professor

" Founder of Galaxies Number Theory, 2021".

## About

60

Publications

3,596

Reads

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68

Citations

Introduction

Fermat's Last Theorem and Galaxies of the Universe

## Publications

Publications (60)

We show that the Diophantine equation X^{3} + Y^{6} = Z^{6} admits matrix triple solutions from M_{3}(N) and M_{6k}(N). We construct infinite universes made of these solutions. We introduce different construction structures sets of matrix solutions associated to the above Diophantine equation. These construction structures sets of matrix solutions...

We define matrix graphs and their construction structures of matrix solutions of Diophantine equations. We introduce matrix networks linked to graph theory. We define complex polynomials over N which don't have any positive integer roots but which have matrix roots with positive integers as entries. We show that these matrix roots are construction...

We prove that the Diophantine equation X ^{p} = Y^{ 2} + I_{ p} , p ≥ 3, admits an infinite number of matrix solutions. We show that the matrix elliptic curve X^{ 2} = Y^{ 3} + I_{3} , and the Diophantine equation X^{2} = Y^{p} + I_{p} , p ≥ 3, admits each an infinite number of matrix solutions. We show that the Diophantine equation X^{n} − Y^{q} =...

We show that the structures of the matrix solutions of the matrix elliptic curves 2 3 6 EY X I : , α = +× ∈ α α allow the construction of the matrix solutions of the equations 4 24 6 24 24 2 24 24 XY ZX IY I Z += − −= ,( )( ) . Mathematics Subject Classification(2010). 15B36, 11D61.

p>We construct the galaxies of sequences of Toeplitz matrix solutions of the Diophantine equation Xn + Y n = Z n , n ≥ 3, linked to Pythagorean triples.</p

We show that the Diophantine equation X^{3} + Y^{6} = Z^{6} (0.1) admits matrix triple solutions from M_{3}(N) and M_{6k}(N), k ∈ N. We construct infinite universes made of these solutions. We introduce different construction structures sets of matrix solutions associated to the Diophantine equation (0.1). These construction structures sets of matr...

We show that the matrix exponential Diophantine equation (X^{ n} − I_{ 2×q×n})(Y^{ n} − I_{ 2×q×n}) = Z^{ 2} , n, q ∈ N, n ≥ 1, q ≥ 2, has an infinite number of matrix solutions in M_{ 2×q×n} (N). We obtain the same result for the Diophantine equation (X^{n} − I_{ 2×m×n})(Y^{ m} − I_{ 2×m×n}) = Z^{ 2} , n, q ∈ N, n ≥ 1, m ≥ 1, in M_{ 2×m×n} (N). We...

We show that the matrix exponential Diophantine equation (Xn - Iqxn)(Yn - Iqxn) = Z2; admits at least 4 x n2 different construction structures of matrix solutions. We also prove that the matrix exponential Diophantine equation (Xn - Inxm)(Ym - Inxm) = Z2; admits at least 4 x n x m different construction structures of matrix solutions in Mnxm(\(\mat...

We show that the structures of the matrix solutions of the matrix elliptic curves E α : Y ^{2} = X^{ 3} + α × I_{ 6} , α ∈ N, allow the construction of the matrix solutions of the equations X ^{4} + Y^{ 24} = Z^{ 6} , (X^{ 24} − I_{ 24})(Y^{ 24} − I_{ 24}) = Z^{ 2}. Mathematics Subject Classification(2010). 15B36, 11D61.

We show that matrix linear (or exponential) Diophantine equations always admit a finite number of construction structures of matrix solutions.
Mathematics Subject Classification(2010). 15B36, 11D72, 11D61.

We prove that the sum of the entries of a positive matrix can be written as the sum of squares. An algorithm, which allows every positive trigonometric polynomial with a sufficiently large constant coefficient to be written as a single square of another trigonometric polynomial, is provided. Also, this algorithm allows us to prove that every positi...

We show that von Neumann's inequality holds for n-tuples of complex lower (or upper) Rare contractions. We construct contractive homomorphism.

We introduce the spectral mapping factorization of tuples of circulant matrices and its matrix version. We prove that every tuple of circulant contractions has a unitary N-dilation. We show that von Neumann's inequality holds for tuples of circulant contractions. We construct completely contractive homomorphisms over the algebra of complex polynomi...

We introduce an algorithm which allows us to prove that there exists an infinite number of sequences of matrix strong Diophantine 27-tuples which induce an infinite number of sequences of matrix elliptic (or hyperelliptic) curves.
Mathematics Subject Classification(2010). 15B36, 11D09, 11G05.

Matrix Solutions of Beal's Conjecture.

We consider the Toda lattice associated to the twisted affine Lie algebra c (1) 2. It is well known that this system is a two-dimensional algebraic completely integrable system. By using algebraic geometric methods, we give a linearisation of the system. Finally, a Lax representation in terms of 2 × 2 matrices is constructed for this system.

We prove that Diophantine quadruples generate block matrix strong Diophantine 81^{ 9}-tuples. We construct block matrix elliptic (or hyperelliptic) curves which have 2 × 81 ^{9} block matrix points.

We construct a sequence of matrix strong Eulerian 2^{ n+3}-tuples with integer coefficients by using the elements of the set {5, 10, 29}. Also, we construct a sequence of matrix elliptic (or hyperelliptic) curves generated by a sequence of matrix strong Eulerian m-tuples.

We introduce clockwise β-Funtions associated to the finite sets of positive integers which allow us to encrypt messages by using β-Functions Key Exchange. We construct a matrix Eulerian semigroup by using a β-function associated to the Eulerian triple {4, 9, 28}. Mathematics Subject Classification(2010). 11D41, 11D09, 11G05.

We introduce finite commutative matrix strong Diophantine groups using δ-function associated to the Diophantine triple S = {1, 3, 8}. We establish the connection between the matrix elliptic curve cryptography and finite commutative matrix strong Diophantine groups. We introduce a new matrix key exchange linked to the matrix elliptic curve cryptogra...

We introduce an algorithm of construction of matrix strong Diophantine 50,301-tuples. We show that there exist infinitely many matrix strong Diophantine 2,530,190,601-tuples. Also, we show that there exist infinitely many matrix strong Diophantine 23 × 3^{ n}-tuples. We construct matrix elliptic (or hyperelliptic) curves. We establish the connectio...

We introduce an algorithm of construction of matrix strong Diophantine 43,740-tuples with positive integers as entries by using the embedding process. We construct matrix elliptic (or hyperelliptic) curves which have at least 87,480 points.

We construct a new family of matrix solutions in M _{m )(N) of the equation X ^{3} + Y^{ 3 }= Z^{ 3} , XY Z = 0. We prove that there exists an infinite number of galaxies of sequences of matrix triples which satisfy the equation X ^{3} + Y^{ 3} = Z^{ 3} , XY Z = 0.

We introduce an algorithm which allows us to prove that there exists an infinite number of matrix strong Diophantine 540-tuples with positive integers as entries. We construct matrix elliptic curves and matrix hyperelliptic curves by using matrix strong Diophantine 540-tuples.

We introduce an algorithm which allows us to prove that there exists an infinite number of matrix strong Diophantine 20-tuples. We show that Diophantine quadruples generate matrix elliptic curves and matrix hyperelliptic curves which have each 20 solutions in M_{ 6 }(N).

We construct matrix Diophantine quadruples which cannot be extended to matrix Diophantine quintuples.

We show that every triple of positive integers generates a matrix solution in M n (N) of the equation X_{1}^{ m} + X_{2}^{ m} +. .. + X_{n-1}^{m} = X_{n}^{m} , m ≥ 2, n ≥ 3. Mathematics Subject Classification(2010). 11D41, 11D25, 03C95.

We show that every triple of positive integers generates a matrix solution in M_{ n }(N) of the equation X^{ n} + Y^{ n} + Z^{ n} = D^{ n} , n ≥ 3. Mathematics Subject Classification(2010). 11D41, 11D25, 03C95.

We show that every triple of positive integers generates a matrix solution in M_{ 9} (N) of the equation X^{ 3} + Y^{ 3} + Z^{ 3} = D^{ 3}. Mathematics Subject Classification(2010). 11D41, 11D25, 03C95.

We construct the galaxies of sequences of Pythagorean quadruplets of spherical Fourier transform of type δ and its associated galaxian rings. We introduce the astral body of the spherical Fourier transformation of type δ and the ring of galaxian rings of sequences of Pythagorean quadruplets of spherical Fourier transform of type δ. Mathematics Subj...

We construct the Toeplitz matrix solutions in M _{n} (N) of the equation X^{ n} + Y^{ n} = Z^{ n} , n ≥ 3, n ∈ N and we introduce the mathematical modelization of the idea of the multiverse by constructing the multiverses F _{n} (M_{ 3nm} (C)) of blocks of Toeplitz matrices. Mathematics Subject Classification(2010). 11C20, 11D45, 11D41.

Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatum in duos ejusdem nominis fas est dividere: cujes rei demonstrationem mirabilem sane detexi. Hane marginis exiguitas non caperet.-Pierre de Fermat (1637). Abstract. We develop an algorithm which allows us to constr...

We develop an algorithm which allows us to construct sequences of triples of complex numbers solutions of the equation x^{n} + y^{ n} = z^{ n} , n ≥ 3. We extend the Fermat Last Theorem. We prove that there exists an infinite number of galaxies of sequences of triples of complex numbers solutions of this equation. We introduce the astral bodies of...

We construct Pythagorean Quadruplets.

We construct the enlargement of the Hankel matrix solutions in M_{ m} (N) of the equation X^{ 9} + Y^{ 9) = Z^{ 9}. Mathematics Subject Classification(2010). 11C20, 11D45, 11D41.

We construct the Toeplitz matrix solutions in M_{ n} (N) of the equation X ^{n} + Y^{ n }= Z^{ n} , n ≥ 3, n ∈ N. Mathematics Subject Classification(2010). 11C20, 11D45, 11D41.

We introduce for the first time the idea of unthinkable equations. We construct the matrix solutions in M_{ m }(N) of the equation X^{ n} + Y^{ n} = Z^{ n} , n ∈ {3;4;6;8;12;16;32;48;64; 96;;192;576;1,728}. We provide the matrix solutions of the equation X^{ 5,184} + Y^{ 5,184} = Z^{ 5,184} by using the galaxies of sequences of matrix Pythagorean t...

Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatum in duos ejusdem nominis fas est dividere: cujes rei demonstrationem mirabilem sane detexi. Hane marginis exiguitas non caperet.-Pierre de Fermat (1637). Abstract. We introduce a new family of matrices which allow...

We introduce a new family of matrices with positive integers as entries which are solutions of the equations X^ 3 + Y^ 3 = Z^ 3 by using the galaxies of sequences of matrix Pythagorean triples. We show that the equations X^ 9 + Y ^9 = Z^ 9 , X^ 27 + Y^ 27 = Z^ 27 , X^ 81 + Y^ 81 = Z^ 81 and X^ 243 + Y^243 = Z^ 243 have each an infinite number of ma...

We construct the galaxies of sequences of Pythagorean triples of spherical Fourier transform of type δ and its associated galaxian rings. We prove that every galaxian ring is associated to a homomorphism of rings. We introduce the astral body of the spherical Fourier transformation of type δ and the motions of the galaxies of sequences of Pythagore...

The factorization of complex polynomials over D n (n > 1) allows us to extend the von Neumann inequality to the setting of the Wiener norm. This extension allows us to prove that von Neumann's inequality hold up to the constant 2 2n for n-tuples of commuting contractions on a Hilbert space. Mathematics Subject Classification(2010). 42A16, 47A68, 11...

We introduce the spectral mapping factorization of tuples of circulant matrices and its matrix version. We show that von Neumann's inequality holds for tuples of circulant contractions and tuples of upper (or lower) complex triangular Toeplitz contractions generated by finite subsets of the unit ball of the algebra of complex polynomials over D. We...

We develop an algorithm which allows us to construct sequences of Pythagorean triples. We prove that there exists an infinite number of galaxies of sequences of Pythagorean triples. We show that every galaxy of sequences of Pythagorean triples is associated to a galaxian semiring and every galaxian semiring is associated to a semiring homomorphism....

We construct sequences of triples of circulant matrices with positive integers as entries which are solutions of the equation. We introduce Mouanda's choice function for matrices which allows us to construct galaxies of sequences of triples of circulant matrices with positive integers as entries. We give many examples of galaxies of circulant matri...

We develop an algorithm which allows us to construct sequences of Pythagorean triples for Fibonacci's sequence. We prove that there exists an infinite number of galaxies of sequences of Pythagorean triples for Fibonacci's sequence. We introduce the astral bodies of the set N for Fibonacci's sequence and we construct the astral bodies of the set of...

We develop an algorithm which allows us to construct sequences of matrix Pythagorean triples of any size. We prove that there exists an infinite number of galaxies of sequences of matrix Pythagorean triples. We show that every galaxy of sequences of matrix Pythagorean triples is associated to a galaxian semiring and every galaxian semiring is assoc...