Short answer

Not in the way the Qur'an was. By the Buddhists' own chronicles, the monks handed the Buddha's teaching down by memory alone. Only later, in Sri Lanka, under King Vattagamani, did they write it down, so that the teaching would not be lost. Wilhelm Geiger, who translated one chronicle, dates this to the first century BCE, more than four hundred years after the Buddha's death. One of them, the Dipavamsa, says that long before then, rival monks had altered the texts, moved discourses about and composed new ones. The Buddha also let monks learn his words each in his own dialect. In its own scripture, the Buddha even says the true teaching would last only five hundred years. The Qur'an was written down as it came, by scribes in the Prophet's (ﷺ) lifetime. His first successor gathered it into one book.

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