Many passages in the Bible show that the first 5 books of the Bible was written by Moses. (Jos. 1:7; Jg. 3:4; 2 Ki. 18:6; Mal 4:4) In addition to David, Luke and John's references, Jesus himself acknowledged that Moses was the writer at Mark 10:3-5 and also at John 5:46, 47.
The closing chapters of the fifth book in question (Deuteronomy) tells of the appointment of Joshua as leader and the death of Moses. So even though the scriptural references and the evidence within the Pentateuch itself shows that its writership properly belongs to Moses, it is clearly with the exception of the closing verses of Deuteronomy.
After writing at length establishing the Mosaic authorship of Deuteronomy, Old Testament scholar Gleason Archer concluded:
"Only chapter 34 is demonstrably post-Mosaic, since it contains a short account of Moses’ decease. But this does not endanger in the slightest the Mosaic authenticity of the other thirty-three chapters, for the closing chapter furnishes only that type of obituary which is often appended to the final work of great men of letters. An author’s final work is often published posthumously (provided he has been writing up to the time of his death). Since Joshua is recorded to have been a faithful and zealous custodian of the Torah, Moses’ literary achievement, it is quite unthinkable that he would have published it without appending such a notice of the decease of his great predecessors." - A Survey of Old Testament Introduction
The closing chapters of the fifth book in question (Deuteronomy) tells of the appointment of Joshua as leader and the death of Moses. So even though the scriptural references and the evidence within the Pentateuch itself shows that its writership properly belongs to Moses, it is clearly with the exception of the closing verses of Deuteronomy.
After writing at length establishing the Mosaic authorship of Deuteronomy, Old Testament scholar Gleason Archer concluded:
"Only chapter 34 is demonstrably post-Mosaic, since it contains a short account of Moses’ decease. But this does not endanger in the slightest the Mosaic authenticity of the other thirty-three chapters, for the closing chapter furnishes only that type of obituary which is often appended to the final work of great men of letters. An author’s final work is often published posthumously (provided he has been writing up to the time of his death). Since Joshua is recorded to have been a faithful and zealous custodian of the Torah, Moses’ literary achievement, it is quite unthinkable that he would have published it without appending such a notice of the decease of his great predecessors." - A Survey of Old Testament Introduction