"Psalms is a book, so technically, Solomon wrote a fraction of a book of Psalms."
Yes, however, I think the intention of the question is how many Psalms did Solomon write. Psalm means song. From the book of Psalms, Solomon wrote 72 and 127. However, we are told in 1 Kings 4:29-34 that Solomon wrote 1,005 songs. We only two songs (Psalm 72 and 127) in the Old Testament unless you also count the book, the Song of Solomon, as the third.
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