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Euler's conjecture: For any positive integer $n$, $8n+3$ can be represented as a sum $$8n+3=(2k-1)^2+2p,$$ where $k$ is a positive integer, and $p$ is a prime.

I want to know whether there has been progress on the problem. Could you recommend some references? Thanks a lot.

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Barry Mazur discussed this problem in his presentation of January 2012, Why is it plausible? Mazur says there that it is still unsettled.

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