Define multiplication as $(a,b) \boxdot (c,d)=(ac-bd(r^2+s^2), ad+bc+2rbd)$ where $a,b,c,d,r\in \mathbb{R}$ and $0\neq s\in \mathbb{R}$.
69721
$(a,b) \mathbin\# (c,d)=(a+c,b+d)$ and $(a,b) \mathbin\&(c,d)=(ac-bd(r^2+s^2), ad+bc+2rbd)$. Multiplicative inverse?
64545
Continuum between addition, multiplication and exponentiation?
137626
If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
1086
What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?
150289
A number with an interesting property. $abcd=a^b c^d$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
152078
What would be the symbol for 'multiplication on division'?
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
25907
Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
89192
$(\mathbb R, \oplus)$ is a group. Define a multiplication with which we get a field. Where $a \oplus b = a + b +1$
154596
When should \cdot be used to indicate multiplication?
146947
A multiplication algorithm found in a book by Paul Erdős: how does it work?
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
25744
Multiplication in Permutation Groups Written in Cyclic Notation