Abstract
We prove that the primes of the form \(x^2+y^2+1\) contain arbitrarily long non-trivial arithmetic progressions.
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Acknowledgements
We are grateful to the anonymous referee for his/her very helpful comments. We also thank Professor Henryk Iwaniec for his helpful explanation on Theorem 1 of [7]. The work is supported by National Natural Science Foundation of China (Grant No. 11671197). The second author is the corresponding author.
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Communicated by J. Schoißengeier.
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The work is supported by the National Natural Science Foundation of China (Grant No. 11671197).
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Sun, YC., Pan, H. The Green–Tao theorem for primes of the form \(x^2+y^2+1\). Monatsh Math 189, 715–733 (2019). https://doi.org/10.1007/s00605-018-1245-0
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DOI: https://doi.org/10.1007/s00605-018-1245-0