Does the Hebrew of Deuteronomy 31:2 indicate that Moses’ date of death was exactly the same as his date of birth, 120 years later?

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A recent answer to an old question of mine said that Deuteronomy 31:2 showed what is called ‘the integral age of the prophets’. I had never heard of this before, so all I can do is give the link, and then the answer posted on 6/1/23 by Johannes can be checked.

The point was made that “Moses says in that verse, ‘I am a son of a hundred and twenty years today’ (Deut 31:2) in the sense that he was turning 120 years old that very day, in which he was later going to die.”

I note that not all translations have “a son of” in the text, and wonder if that is significant? It is, however, in Young’s Literal Translation of 1898, worded as, “A son of a hundred and twenty years [am] I to-day”.

… and he saith unto them, A son of a hundred and twenty years `am’ I to-day; I am not able any more to go out and to come in, and Jehovah hath said unto me, Thou dost not pass over this Jordan, [Deuteronomy 31:2 YLT]

I have no problem with Moses dying aged 120 years, or even being precisely 120 years old on the day of his death, but I don’t understand the suggestion that he was born on that same day and month, 120 years earlier. Is there anything in the text to suggest that Moses’ date of birth would correspond exactly to his date of death, a one-hundred-and-twenty-years gap inbetween? Or is that an understanding of the Jewish scribes, or an ancient tradition – that Moses’ birth day and month was exactly the same as his death day and month?

I am not asking about the topic of dates of birth and death with all the prophets having that correspondence – what some seem to call “the integral age of the prophets”. Or, have I quite misunderstood that point in the answer recently given to my old question?