Applications of the Counterfactual Method to Problems in Number Theory

Weisi Tang; Yunkun Song

Authors

Weisi Tang Chengdu Foreign Language School, Chengdu, Sichuan, 610000, China Author
Yunkun Song Sendelta International Academy, Shenzhen, Guangdong, 518129, China Author

Keywords:

inverse method, number theoretic problems, applied analysis

Abstract

The counterfactual method, which involves assuming the negation of a given proposition and deducing logical contradictions, serves as a powerful tool in solving problems in number theory. By carefully identifying and analyzing false assumptions, this method demands rigorous logical reasoning and strict avoidance of circular arguments. Its application not only helps verify the validity of mathematical statements but also fosters deeper insight into the structure of numerical relationships. Moreover, the method sharpens one’s ability to think critically and systematically, thereby contributing to both theoretical advancements and the cultivation of mathematical thinking.

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