Charles Halton recently wrote a blogpost that follows in the footsteps of some scholars, like Walter Brueggemann, that argues that Genesis is not a foundational book for the rest of the Old Testament. Both Halton (http://awilum.com/?p=2063) and Brueggemann (Genesis, 41) make the same argument that can be summarized as follows:
The rest of the Old Testament doesn't mention the characters and events in the book of Genesis in any length or detail. Hence, the book was not seen as foundational to the authors of the rest of the Hebrew Bible.
Now, I'm going to assume that we all three agree that Genesis was not written until after the prophets, the Deuteronomistic History (including the legal material in D and in the BC---I'm not sure if they would agree with the latter). The only books written after Genesis that I can think of are books indisputably identified by scholars to be postexilic, like Ecclesiastes, Daniel, Chronicles, Job, etc.
Wisdom books like Ecclesiastes often don't allude to historical events and people, as they tend to focus on what to make of life in the now. Daniel is apocalyptic and uses the prophet Daniel in the time of the exile, rather than a patriarch to present its eschatology. Ironically, Chronicles does allude to Adam in its chronology, but it's purposes are not to do anything in terms of retelling the story (one might say that the historical framework can be cast in those terms, but it is not explicit). Job, ironically, in one way or another, is linked to the argument in some way (although it is not known whether Genesis is clarifying Job or Job is clarifying Genesis (I think it's likely the latter).
But the problem with this line of inquiry is that it misses the point of Genesis altogether. When we ask whether Genesis is foundational for the rest of the Bible, we need to understand that Genesis is largely written afterward, so instead the question should be, "Does the teaching of Genesis function as foundational to the rest of the canon?"
In other words, since Genesis is written afterward, one must ask whether it in some way functions as foundational for believers to understand the rest of the Bible. Here's why I think it does.
Genesis puts forth the creation principle upon which the rest of the Bible rests its assertions. In that regard it summarizes what is said in the law and prophets in terms of that principle. The law may speak of doing good, and the prophets may speak of being faithful to YHWH as creator within the threat of chaos, but Genesis gives the foundational principle for what is said therein.
Genesis also fills out the prehistory of Israel that likely existed only within certain written and oral traditions and crafts them into a single book that helps convey a theology that lays the foundation for understanding the rest of Scripture in terms of who God is, His purposes in creation, the dual perspectives that exist in the world (divine and human) when assessing the power of chaos to destroy and God's goodness to limit and focus its power toward good/salvation, and the role of God's covenant people in the world. Hence, it provides not only a historical foundation for the rest of the Bible, but a foundational/worldview in which the rest of the Bible can be contextualized.
In this sense, the rest of the Bible really has no coherence without Genesis, and that is why it has functioned as the foundational book for the rest of Israelite literature (including that found within the Pseudepigrapha and DSS) since its creation. Genesis brings together the rest of biblical literature, not because it precedes it, and is therefore quoted by that literature (how could it be when it doesn't exist yet?), but because it draws it all together under its history and worldview.
Now, Charles does consider that this is important for a canonical argument,
and I would say, "Well, that is how believers view the Bible, so to criticize
one for saying such is to admit that the criticism within that context
is unfounded." But I think the larger argument is that the individual
books don't need Genesis to function as foundational for them, and I
would also disagree with this. The principles and worldview that Genesis teaches is assumed by all of these books, so that when Genesis comes along and makes these assumptions explicit, it gives an explicit voice to what is already implicitly there.
Hence, asking whether the rest of the Bible mentions Adam, or counting how many times the name Abraham is used, or how many times the fall is referred to, is barking up the wrong tree. The theology of Genesis can be seen throughout the canon (as a whole but also individually within the books therein), and it draws from each of those books and provides the proper framework in which to see them all both separately and in unity.