On the consecutive square-free values of the polynomials $$x_1^2+\cdots +x_k^2+1$$, $$x_1^2+\cdots +x_k^2+2$$
Author:
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics
Link
https://link.springer.com/content/pdf/10.1007/s13226-022-00292-z.pdf
Reference12 articles.
1. L. Carlitz, On a problem in additive arithmetic $$(II)$$, Quart. J. Math. 3(1) (1932) 273–290.
2. S. I. Dimitrov, On the number of pairs of positive integers $$x, y\le H$$ such that $$x^2+y^2+1$$, $$x^2+y^2+2$$ are square-free, Acta Arith. 194(3) (2020) 281–294.
3. S. I. Dimitrov, Pairs of square-free values of the type $$n^2+1$$, $$n^2+2$$ , Czechoslovak Math. J. 71(4) (2021) 991–1009.
4. T. Estermann, Einige S$$\ddot{a}$$tze $$\ddot{u}$$ber quadratfreie Zahlan, Math. Ann. 105 (1931) 653–662.
5. D. R. Heath-Brown, The square sieve and consecutive square-free numbers, Math. Ann. 266 (1984) 251–259.
Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Square-Free Numbers of the Form $$\mathbf{x^2+y^2+z^2+z+1}$$ and $$\mathbf{x^2+y^2+z+1}$$;Mathematical Notes;2023-12
2. On the consecutive k-free values for certain classes of polynomials;Periodica Mathematica Hungarica;2023-08-10
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