Narkissos....Thanks for pointing out the obvious to scholar. Without using any English translation, the parallels between John 8:24, 28, 13:19 and Isaiah 43:10 LXX are quite apparent:
Isaiah 43:10: "...hina gnóte kai pisteuséte kai sunete hoti egó eimi..."John 8:24: "ean gar me pisteuséte hoti egó eimi..."
John 8:28: "...tote gnósesthe hoti egó eimi."
John 13:19: "...hina pisteuséte hotan genétai hoti egó eimi."
The high density of "I am" expressions in John is reminiscent of the frequency of egó eimi in Isaiah 40-55 LXX (cf. 41:4, 43:10, 43:25, 46:4, 47:8, 10, 52:6, 45:18, 51:12), which exclusively have divine reference or occur in imitation of divine usage. The blasphemous imitative examples of absolute egó eimi in Isaiah 47:8, 10 (which clearly are patterned after 45:18, 47:8 and Deuteronomy 32:29) echo Yahweh's declarations and indicate it is a feature of divine language. John 8:58 is connected to Isaiah by constituting the third example of unmodified and absolute egó eimi in ch. 8, the previous two examples being verbally allusive of Isaiah 43:10, and Isaiah 43:10-13 is thematically connected to John 8:58 by stressing God's eternity. Isaiah 43:13 (MT) is also verbally similar: "From ancient days (gm-mywm) I am ('ny hw')". (Compare KJV, "Before the day was, I am he"). When I have a chance I'm going to check Theodotion and Symmachus to see how this is rendered. Another clear parallel with John 8:58 is Psalm 90:2 LXX: "Before the mountains came into existence (pro tou oré genéthénai) ... you are (su ei)". Note that in this case there is a contrast in tense and both use the present to indicate God's continuing eternal existence. These are very illuminative of John 8:58. If one looks only at this verse without its broader context (the rest of ch. 8), it is easy to miss these striking resemblances.