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Interested in elementary algebra enter image description hereproblems, and teaching.


2d
awarded  Constituent
Dec
14
comment Find smallest $x$ such that $a^x \equiv b \bmod p$
Yes, sometimes explicit formula or closed formula is not exactly computationally usable: the formula for Euler's totient in terms of prime power factorisation.
Dec
14
comment Find smallest $x$ such that $a^x \equiv b \bmod p$
As already commented by Sal any closed formula would cause the collapse of lot of encryption scheme that rests on the computational difficulty of the "Discrete Logarithm Problem"
Dec
10
awarded  Caucus
Nov
21
comment Most ambiguous and inconsistent phrases and notations in maths
You are right. $\mathbf{Z/nZ}$ and $ \mathbf{Z}$ are closer in the sense of being monogenic (generated by a single element) but not in the sense of exhibiting periodic (cyclic) behaviour. A crow and a human could not both be called mammals because crow is not a mammal. But they can both be called bipeds for having two feet.
Nov
21
comment Most ambiguous and inconsistent phrases and notations in maths
About trees: Mathematicians try to name things by analogy. Trees of botanical kind, after shedding their leaves, resemble those of combinatorial kind and are perfectly valid. I think OP wanted to know if the analogy behind the name actually contradicts the concept it tries to illustrate.
Nov
21
comment Most ambiguous and inconsistent phrases and notations in maths
When we place an adjective in front a noun (or after it if you are French!) it may signify something less than, or more than, or a variant of the object that noun symbolises. (Virtual keyboard is not a keyboard.) So, IMO, outer measure is a perfectly valid choice.
Nov
21
comment Most ambiguous and inconsistent phrases and notations in maths
@ Mariano Su\'arez-Alvarez: The title of the post says "inconsistent phrase" and the phrase "cyclic group" for a group where there is no periodicity definitely qualifies for it.
Nov
20
answered Most ambiguous and inconsistent phrases and notations in maths
Nov
18
answered If the number $x$ is algebraic, then $x^2$ is also algebraic
Oct
27
answered there exists a diagonalizable linear transformation
Oct
25
answered The set of all finite sequences of members of a countable set is also countable
Oct
25
comment Intuitive Meaning of Quotient Ring
@Magnus: Nice to know it benefits you. Now the correct technical defintion of quotient is to introduce equivalence relation; (in my example having the same last digit). The relations behaves in such a way that when you pick an element each from two equivalence classes and do the addition (or multiplcation) in the ring the resulting element falls in the same equivalence class irrespective of the choices made.
Oct
24
answered Intuitive Meaning of Quotient Ring
Oct
11
answered If $P$ is a projection operator, is $1-P$ also a projection operator?
Sep
24
awarded  Autobiographer
Jul
13
comment Can an analytic function take a simply connected region to a non simply connected region?
You are right; my answer is the same as yours with less details.
Jul
12
answered Can an analytic function take a simply connected region to a non simply connected region?
Jul
11
answered Eigenvectors of two matrices whose sum is an identity matrix?
Jul
9
answered How to solve $b^2-a^2=d^2-c^2$