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Here are the three verses in the Authorized Version that references "birthdays".
Depending on the Bible edition
birth-day
birth day
birthday
Genesis 40:20 (KJV)
And it came to pass the third day, which was Pharaoh's birthday,
that he made a feast unto all his servants:
and he lifted up the head of the chief butler and of the chief baker among his servants.
Matthew 14:6 (KJV)
But when Herod's birthday was kept,
the daughter of Herodias danced before them,
and pleased Herod.
Mark 6:21 (KJV)
And when a convenient day was come,
that Herod on his birthday made a supper to his lords,
high captains, and chief estates of Galilee;
Afaik, this is indicated in Bible texts in many languages, Greek, Latin, Syriac etc.
These are commonly quoted to show that birthdays were a practice in pagan religions. And connected with tragedies.
And it is argued that a pagan element was added to Christianity in the 4th century when Dec 25, or a nearby date, became a birthday celebration.
It is an interesting question as to whether this pagan connection was noted by Christian writers throughout the early centuries? (Definitely there was Puritan-style resistance to Christmas, but that was later.)
And I don't think there is a real case against these pagan birthdays occurring, as seems to be implied in the Russian article.
Steven