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We study the solvability of the Fermat's matrix equation in some classes of 2-by-2 matrices. We prove the Fermat's matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices.
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참고문헌 (15)
참고문헌 신청
A. Aigner / 1934 / Uber die M¨oglichkeit von x 4 + y 4 = z 4in quadratischen K¨orpern / Jber. Deutsch. Math.-Verein 43:226~229
Alexander Aigner / 1957 / Die Unmöglichkeit von x6+y6=z6 und x9+y9=z9 in quadratischen Körpern / Monatshefte für Mathematik 61(2):147~150
Zhenfu Cao / 1998 / Fermat's type equations in the set of 2×2 integral matrices / Tsukuba Journal of Mathematics 22(3):637~643
R. Z. Domiaty / 1966 / Solutions of x 4 + y 4 = z 4 in 2 × 2 Integral Matrices / The American Mathematical Monthly 73(6):631
Nuno Freitas / 2015 / Fermat’s last theorem over some small real quadratic fields / Algebra & Number Theory 9(4):875~895
Alexander Aigner / 1957 / Die Unmöglichkeit von x6+y6=z6 und x9+y9=z9 in quadratischen Körpern / Monatshefte für Mathematik 61(2):147~150
Zhenfu Cao / 1998 / Fermat's type equations in the set of 2×2 integral matrices / Tsukuba Journal of Mathematics 22(3):637~643
R. Z. Domiaty / 1966 / Solutions of x 4 + y 4 = z 4 in 2 × 2 Integral Matrices / The American Mathematical Monthly 73(6):631
Nuno Freitas / 2015 / Fermat’s last theorem over some small real quadratic fields / Algebra & Number Theory 9(4):875~895
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