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Achievement motivation and its relationship with learning is well understand, but is relatively unexplored in discourse surrounding Generative Artificial Intelligence (AI). This study bridges this gap by utilizing a k-means cluster analysis on student data from an AI writing assistant. Analysis revealed three statistically distinct profiles: AI Reliance, characterized by frequent and comprehensive use; High Selectivity, defined by highly efficient, high-volume text generation; and Moderate Integration, who engaged minimally across all metrics. A chi-squared test confirmed a significant association between profile membership and the depth of AI integration. These findings suggest that student engagement with AI is not uniform but conforms to distinct, goal-oriented patterns that can be interpreted through the lens of achievement motivation.