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Bajević scored 29 goals in his international career, a testament to his exceptional goal-scoring prowess. He represented Yugoslavia from 1980 to 1990, earning 70 caps and establishing himself as one of the most prolific strikers in the country's history. His goals played a crucial role in Yugoslavia's success during that era, including their victory at the 1984 Summer Olympics and their fourth-place finish at the 1990 FIFA World Cup.