中文摘要：

目的探讨早期代数数论的产生和发展。方法文献考证与概念分析。围绕高次互反律和费尔马大定理,分析其中关键的唯一因子分解问题。结果数论是由整数论过渡到复整数论,又从复整数论发展为应用广泛的代数数论。结论早期的代数数论是随着复整数、理想数等新的代数工具的引入应运而生的。

英文摘要：

Aim To discuss the early history of algebraic number theory.Methods Literature research and concept analyzing.Analysis of the key problem of unique factorization by the law of higher reciprocity and Fermat last theorem.Results Algebraic number theory develops from integer theory to complex integer theory and then from complex integer theory to widely-applied algebraic number theory.Conclusion Algebraic number theory arises with the introduction of some new algebraic tools such as complex integers and ideal number.