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On Matrix Solutions of the Diophantine Equation X 4 n + Y 4 n = Z 4 n , X , Y , Z ∈ M 4 n ( ℕ ) , and Interconnections between Universes of Matrix Triples
UFR-MI, Mathematics and Applications Laboratory, Félix Houphouët-Boigny University, Abidjan, Côte d’Ivoire
UFR-MI, Mathematics and Applications Laboratory, Félix Houphouët-Boigny University, Abidjan, Côte d’Ivoire
Mathematics Department, Blessington Christian University, Nkayi, Republic of Congo
UFR-MI, Mathematics and Applications Laboratory, Félix Houphouët-Boigny University, Abidjan, Côte d’Ivoire
- 1 UFR-MI, Mathematics and Applications Laboratory, Félix Houphouët-Boigny University, Abidjan, Côte d’Ivoire
- 2 UFR-MI, Mathematics and Applications Laboratory, Félix Houphouët-Boigny University, Abidjan, Côte d’Ivoire
- 3 Mathematics Department, Blessington Christian University, Nkayi, Republic of Congo
- 4 UFR-MI, Mathematics and Applications Laboratory, Félix Houphouët-Boigny University, Abidjan, Côte d’Ivoire
Advances in Pure Mathematics·Volume 16 (2026)·Pages 308–317·Published 30 April 2026·DOI10.4236/apm.2026.164015
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Abstract
Let n be a non-zero positive integer, we show that the Diophantine equation X 4 n + Y 4 n = Z 4 n admits an infinite number of matrix solutions in the set M 4 n ( ℕ ) . We introduce different relationships between universes.
KeywordsMatricesPythagorean Triples
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