• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.345-353
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• 2023

Reduced solutions of size 2 and degree n of the Tarry-Escott problem over M₂(ℚ) are determined. As an application, the diophantine equation αAⁿ + βBⁿ = αCⁿ + βDⁿ, where α, β are rational numbers satisfying α + β ≠ 0 and n ∈ {1, 2}, is completely solved for A, B, C, D ∈ M₂(ℚ).