# Beyond ideals in the Dickson ring of integral octonions

@inproceedings{ChaitinChatelin2004BeyondII, title={Beyond ideals in the Dickson ring of integral octonions}, author={Françoise Chaitin-Chatelin}, year={2004} }

This is ongoing work on hypercomputation [4]. We revisit the works of Dickson [5] and Mahler [9] on integral octonions. Nonassociativity (in the form of alternativity) leads to the unexpected consequence that the theorem of (at most) 4 squares (Bachet – Lagrange) becomes a theorem of (exactly) 1, 2 or 4 identical squares for a subset of N∗. These numbers measure the norm of the vectors in the Dickson ring of integral octonions for which the associator (with 3 or 7 pairs of distinct imaginary… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-9 OF 9 REFERENCES

## The Octonions

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Ideals in cayley’s algebra

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## On ideals in the Cayley – Dickson algebra

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## A new simple theory of hypercomplex integers

VIEW 14 EXCERPTS

HIGHLY INFLUENTIAL

## Vorlesungen über die Zahlentheorie der Quaternionen

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## On Quaternions and Octonions

VIEW 3 EXCERPTS

## Ideals in the Integral Octaves

VIEW 3 EXCERPTS

## An Introduction to the Theory of Numbers

VIEW 2 EXCERPTS