Number Theory: A Very Short Introduction by Robin Wilson

Author:Robin Wilson
Language: eng
Format: epub
ISBN: 9780192519078
Publisher: Oxford University Press
Published: 2020-05-27T23:00:00+00:00

These in turn lead to the simultaneous linear congruences or 1 (mod 8) and or 1 (mod 125), and on examining these in pairs, as above, we find that the only 3-digit self-replicating numbers are and 625, with and .

Squares and non-squares

We conclude this chapter by looking at some more quadratic congruences. Our explorations will lead us to one of the most important results in number theory, the law of quadratic reciprocity.

We’ll start with the congruence

We can solve this by multiplying by 4 and adding 9 to both sides, giving

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