Abstract
In this last chapter devoted to Number Theory, we return to the analysis of the congruence a k ≡ 1 (mod n), concentrating ourselves in two distinct problems, briefly discussed below.
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Notes
- 1.
The coming items are based on the solution of Professor Samuel B. Feitosa.
- 2.
Cf. Problem 6, page 190.
- 3.
- 4.
After Johann Carl Friedrich Gauss , German mathematician of the eighteenth and nineteenth centuries. Gauss is generally considered to be the greatest mathematician of all times. In the several different areas of Mathematics and Physics in which he worked, like Algebra, Analysis, Differential Geometry, Electromagnetism and Number Theory, there are always very important and deep results or methods that bear his name. We refer the reader to [38] for an interesting biography of Gauss.
- 5.
For a more general result, see Theorem 20.19.
- 6.
For a natural proof of such an identity, we refer the reader to item (f) of Problem 10, page 327.
- 7.
We follow the steps delineated in problem XI.14 of the marvelous book [32].
References
J.H.E. Cohn, Square Fibonacci numbers, etc. Fibon. Quart. 2, 109–113 (1964)
J. Roberts, Elementary Number Theory: a Problem Oriented Approach. (MIT Press, Cambridge, 1977)
M.B.W. Tent, Prince of Mathematics: Carl Friedrich Gauss (A.K. Peters Ltd, Wellesley, 2006)
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Caminha Muniz Neto, A. (2018). Primitive Roots and Quadratic Residues. In: An Excursion through Elementary Mathematics, Volume III. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-77977-5_12
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