The law of quadratic reciprocity

2010 ◽  
pp. 23-30
Author(s):  
Martin Aigner ◽  
Günter M. Ziegler
Keyword(s):  
Quadratic Reciprocity ◽  
The Law

scholarly journals On the law of quadratic reciprocity

1935 ◽  
Vol 41 (6) ◽  
pp. 359-361 ◽  
Author(s):  
Albert Whiteman
Keyword(s):  
Quadratic Reciprocity ◽  
The Law

The law of quadratic reciprocity

2018 ◽  
pp. 27-34
Author(s):  
Martin Aigner ◽  
Günter M. Ziegler
Keyword(s):  
Quadratic Reciprocity ◽  
The Law

scholarly journals A Minimalist Proof of the Law of Quadratic Reciprocity

2019 ◽  
Vol 126 (10) ◽  
pp. 928-928
Author(s):  
Bogdan Veklych
Keyword(s):  
Quadratic Reciprocity ◽  
The Law

The 152-nd Proof of the Law of Quadratic Reciprocity

1963 ◽  
Vol 70 (4) ◽  
pp. 397 ◽  
Author(s):  
Murray Gerstenhaber
Keyword(s):  
Quadratic Reciprocity ◽  
The Law

On Legendre’s Work on the Law of Quadratic Reciprocity

2011 ◽  
Vol 118 (3) ◽  
pp. 210
Author(s):  
Steven H. Weintraub
Keyword(s):  
Quadratic Reciprocity ◽  
The Law

4. Congruences, clocks, and calendars

2020 ◽  
pp. 58-78
Author(s):  
Robin Wilson
Keyword(s):  
Chinese Remainder Theorem ◽  
Quadratic Reciprocity ◽  
Mersenne Numbers ◽  
Linear Congruences ◽  
Day Of The Week ◽  
The Law

‘Congruences, clocks, and calendars’ demonstrates how we might apply the idea of congruence, first introduced by Gauss in 1801, to problems such as testing which Mersenne numbers are primes and finding the day of the week on which a given date falls. Ancient Chinese puzzles depended on the solving of simultaneous linear congruences, inspiring mathematicians and giving rise to the Chinese Remainder Theorem. Exploring quadratic congruences leads towards the law of quadratic reciprocity, noted by Euler and Legendre and proved by Gauss. The problem, ‘Is 1066 a square or a non-square?’ can be solved by applying this law several times to reduce the numbers involved.

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