Notes on Dickson’s Conjecture
نویسنده
چکیده
In 1904, Dickson [5] stated a very important conjecture. Now people call it Dickson’s conjecture. In 1958, Schinzel and Sierpinski [14] generalized Dickson’s conjecture to the higher order integral polynomial case. However, they did not generalize Dickson’s conjecture to the multivariable case. In 2006, Green and Tao [13] considered Dickson’s conjecture in the multivariable case and gave directly a generalized Hardy-Littlewood estimation. But, the precise Dickson’s conjecture in the multivariable case does not seem to have been formulated. In this paper, based on the idea in [15], we will try to complement this and give an equivalent form of Dickson’s Conjecture, furthermore, generalize it to the multivariable case or a system of affine-linear forms on N . We also give some remarks and evidences on conjectures in [15].
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