关于欧拉勒让德符号公式发表出处及欧拉判别法首次发表文献的技术问询

Hey there! Great question about tracking down Euler's original publication of his criterion—this is such a common pain point with older mathematical works, so I totally get where you're coming from.

Let me break down what I know:

• Euler's criterion was first formally published in his 1775 paper Theorematum quorundam ad numeros primos spectantium demonstratio. While this is the first public, peer-reviewed appearance, Euler actually discussed the core ideas earlier (around 1747-1748) in private letters to Goldbach—those aren't considered formal publications though.
• To access the original work, your best bets are:
  • Checking the collected works of Euler, known as Opera Omnia. This paper is included in the number theory section (Series 1, Volume 2), and most university math libraries will have physical or digital copies of the full set.
  • Looking for digitized versions in institutional math archives (many universities host scans of classic mathematical texts in their local digital collections).
  • If you can't get direct access to the original paper, number theory history texts like Dickson's History of the Theory of Numbers (Volume 1) provide detailed references and discussions of Euler's work here, which can help you verify the context and content.

It's totally normal that MathSciNet doesn't link to this—its focus is more on modern journal literature, and many of Euler's key works are contained in his collected volumes or older 18th-century journals that aren't fully integrated into their linking system.

备注：内容来源于stack exchange，提问作者Lereu