Around 1637, Fermat wrote his Last Theorem in the margin of his copy “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, int...Around 1637, Fermat wrote his Last Theorem in the margin of his copy “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”. With n, x, y, z <span style="white-space:nowrap;">∈ N (meaning that n, x, y, z are all positive numbers) and n > 2, the equation x<sup>n</sup> + y<sup>n</sup> = z<sup>n</sup><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 “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”. With n, x, y, z <span style="white-space:nowrap;">∈ N (meaning that n, x, y, z are all positive numbers) and n > 2, the equation x<sup>n</sup> + y<sup>n</sup> = z<sup>n</sup><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.
