A ring is a set R equipped with two binary operations + and · satisfying the following three sets of axioms, called the ring axioms
R is an abelian group under addition, meaning that:
(a + b) + c = a + (b + c) for all a, b, c in R (that is, + is associative).
a + b = b + a for all a, b in R (that is, + is commutative).
There is an element 0 in R such that a + 0 = a for all a in R (that is, 0 is the additive identity).
For each a in R there exists −a in R such that a + (−a) = 0 (that is, −a is the additive inverse of a).
R is a monoid under multiplication, meaning that:
(a · b) · c = a · (b · c) for all a, b, c in R (that is, · is associative).
There is an element 1 in R such that a · 1 = a and 1 · a = a for all a in R (that is, 1 is the multiplicative identity).
Multiplication is distributive with respect to addition, meaning that:
a ⋅ (b + c) = (a · b) + (a · c) for all a, b, c in R (left distributivity).
(b + c) · a = (b · a) + (c · a) for all a, b, c in R (right distributivity).
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呢個set equip埋正正常常既一堆運算 會form一個叫Q(sqrt(d))既ring 英文叫做quadratic integer (d mod 4=1個時有啲唔同 但係作為introductory 我地忽略細節唔講)
phi同pho既分子都係a+b sqrt(5)既form where a,b are integer
有個特性 係佢地既任何正整數次方都係a+b sqrt(d) form 對計binet既作用好trivial
其他ring既特性係呢個討論無用