EXPERIMENT is one of the necessary conditions for scientific progress.For cognitive science,neuroscience,biomedical science and other human-related disciplines,experiments involving human subjects can confirm or dispr...EXPERIMENT is one of the necessary conditions for scientific progress.For cognitive science,neuroscience,biomedical science and other human-related disciplines,experiments involving human subjects can confirm or disprove scientific hypotheses in a controlled and systematic manner,while establishing causal relationships between studied variables.These experiments also provide both qualitative and quantitative analysis capable of statistically identifying significant patterns.Thus,solid experiments directly support testable and replicable scientific conclusions.However,limited by the budget as well as the available candidate group,current experiment design selects random subjective in an arbitrary scale,bringing a question that how they can stand for the whole studied population.展开更多
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
基金supported in part by National Natural Science Foundation of China(62476270,62076237)。
文摘EXPERIMENT is one of the necessary conditions for scientific progress.For cognitive science,neuroscience,biomedical science and other human-related disciplines,experiments involving human subjects can confirm or disprove scientific hypotheses in a controlled and systematic manner,while establishing causal relationships between studied variables.These experiments also provide both qualitative and quantitative analysis capable of statistically identifying significant patterns.Thus,solid experiments directly support testable and replicable scientific conclusions.However,limited by the budget as well as the available candidate group,current experiment design selects random subjective in an arbitrary scale,bringing a question that how they can stand for the whole studied population.
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.
