The Euclidean algorithm has been known for over 2000 years and has always been a favorite among number theorists. After these many years, there is now a potential competitor, invented by J. Stein in...

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Answered Same DayDec 24, 2021

Answer To: The Euclidean algorithm has been known for over 2000 years and has always been a favorite among...

David answered on Dec 24 2021
124 Votes
We can define the relationship as
a = n  a/n + (a mod n)
Thus, we can define the mod oper
ator as: a mod n = a – n  a/n
a. 5 mod 3 = 5 – 3 5/3 = 2
b. 5 mod –3 = 5 – (–3) 5/(–3) = –1
c. –5 mod 3 = –5 – 3 (–5)/3 = 1
d. –5 mod –3 = –5 – (–3) (–5)/(–3) = –2
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