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We examine how preservice teachers interact with generative AI tools to solve a mathematical problem involving cost optimization and common multiples. Conducted in a hybrid number theory course, the study analyzes student–AI dialogue transcripts and student performance on follow-up assessments. Using open and axial coding, we identified distinct patterns of engagement, ranging from passive adoption to critical thinking. Findings reveal that students who actively engaged with AI and retained ownership of their reasoning showed stronger problem-solving performance. In contrast, students who accepted AI responses uncritically were more likely to struggle. Implications are discussed for integrating AI in mathematics teacher education, with attention to fostering critical AI use, metacognitive skills, and pedagogical readiness for future classrooms.