Only recorded in Matthew and Luke.
Not recorded in Mark because the perfect Servant is immune to temptation.
Not recorded in John because the pre-existent Son of God cannot be tempted.
Matthew's Perspective
(A) Turn stones to bread in the wilderness
(B) Cast Thyself down at the pinnacle of the temple
(C) Worship Satan at an exceeding high mountain
Luke's Perspective
(A) Turn stones to bread in the wilderness
(C) Worship Satan at an exceeding high mountain
(B) Cast Thyself down at the pinnacle of the temple
Matthew's account of the temptation is based on the historical order. Each temptation by Satan is recorded chronologically. This is evidenced by the words "then" and "again" in Matt 4:1,5,8,10,11.
Notice that in Luke's account, the order of the second and third temptations has been reversed. This is because Luke took a moral perspective of the temptation that is parallel to what is described in Genesis 3:6 and 1 John 2:16.
(A) The lust of the flesh - the tree was good for food
(C) The lust of the eyes - it was pleasant to the eyes
(B) The pride of life - a tree to be desired to make one wise
Reader, you do well to note that all temptations you face come in the above form.
Here are some outlines
(A) Satisfy yourself (Appetite) - Body, misuse of sustenance
(B) Show yourself (Adventure) - Soul, misuse of scripture
(C) Spare yourself (Ambition) - Spirit, misuse of service
1Thess. 5:23
And the very God of peace sanctify you wholly; and I pray God your whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ.