Around 1637, Fermat wrote his Last Theorem in the margin of his copy “<em>It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the s...Around 1637, Fermat wrote his Last Theorem in the margin of his copy “<em>It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers</em>”. With <em>n, x, y, z</em> <span style="white-space:nowrap;">∈</span> <strong>N</strong> (meaning that <em>n, x, y, z</em> are all positive numbers) and <em>n</em> > 2, the equation <em>x<sup>n</sup></em> + <em>y<sup>n</sup></em> = <em>z<sup>n</sup></em><sup> </sup>has no solutions. In this paper, I try to prove Fermat’s statement by reverse order, which means no two cubes forms cube, no two fourth power forms a fourth power, or in general no two like powers forms a single like power greater than the two. I used roots, powers and radicals to assert Fermat’s last theorem. Also I tried to generalize Fermat’s conjecture for negative integers, with the help of radical equivalents of Pythagorean triplets and Euler’s disproven conjecture.展开更多
Gilad Gour and Nolan R Wallach [J. Math. Phys. 51 112201(2010)] have proposed the 4-tangle and the square of the I concurrence. They also gave the relationship between the 4-tangle and the square of the I concurrence....Gilad Gour and Nolan R Wallach [J. Math. Phys. 51 112201(2010)] have proposed the 4-tangle and the square of the I concurrence. They also gave the relationship between the 4-tangle and the square of the I concurrence. In this paper, we give the expression of the square of the I concurrence and the n-tangle for six-qubit and eight-qubit by some local unitary transformation invariant. We prove that in six-qubit and eight-qubit states there exist strict monogamy laws for quantum correlations. We elucidate the relations between the square of the I concurrence and the n-tangle for six-qubit and eight-qubits. Especially, using this conclusion, we can show that 4-uniform states do not exist for eight-qubit states.展开更多
文摘Around 1637, Fermat wrote his Last Theorem in the margin of his copy “<em>It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers</em>”. With <em>n, x, y, z</em> <span style="white-space:nowrap;">∈</span> <strong>N</strong> (meaning that <em>n, x, y, z</em> are all positive numbers) and <em>n</em> > 2, the equation <em>x<sup>n</sup></em> + <em>y<sup>n</sup></em> = <em>z<sup>n</sup></em><sup> </sup>has no solutions. In this paper, I try to prove Fermat’s statement by reverse order, which means no two cubes forms cube, no two fourth power forms a fourth power, or in general no two like powers forms a single like power greater than the two. I used roots, powers and radicals to assert Fermat’s last theorem. Also I tried to generalize Fermat’s conjecture for negative integers, with the help of radical equivalents of Pythagorean triplets and Euler’s disproven conjecture.
文摘Gilad Gour and Nolan R Wallach [J. Math. Phys. 51 112201(2010)] have proposed the 4-tangle and the square of the I concurrence. They also gave the relationship between the 4-tangle and the square of the I concurrence. In this paper, we give the expression of the square of the I concurrence and the n-tangle for six-qubit and eight-qubit by some local unitary transformation invariant. We prove that in six-qubit and eight-qubit states there exist strict monogamy laws for quantum correlations. We elucidate the relations between the square of the I concurrence and the n-tangle for six-qubit and eight-qubits. Especially, using this conclusion, we can show that 4-uniform states do not exist for eight-qubit states.
