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3h
comment Not able to understand the procedure used to find GCD of two numbers through Euclid's algorithm.
@Michael It is also mentioned here in many of my posts, e.g. this one which gives a conceptual presentation.
3h
comment Not able to understand the procedure used to find GCD of two numbers through Euclid's algorithm.
@Michael That's the subtractive form of the Euclidean algorithm which goes back to Euclid. Search Google Books for "subtractive Euclidean algorithm" for expositions, e.g. Stillwell, Elements of Number Theory p.22ff
1d
comment matrix representations and polynomials
This is a special case of circulant algebra, e.g. see this answer.
2d
revised Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
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2d
comment polynomial modulo for higher degree
@Elaqqad mod $\,u,v\,$ is the congruence associated to the ideal $\,I = (u,v)\,$ in the ambient ring $R$, i.e. $\,a\equiv b\pmod{u,v}\,$ $\iff$ $ a-b\in (u,v) = u R + v R\,$ $\iff$ $\, a/I = b/I\,$ in $\,R/I.\ \ $
Jul
3
comment Let $f(x)$ be a polynomial such that $f(a)=b, f(b)=c, f(c)=a$ Then Prove that $a=b=c$.
Exact duplicate of this question.
Jul
3
comment Are there any divisibility rules using 7?
The Universal Divisibility Test is quite simple (and memorable!) $\ \ $
Jul
2
awarded  Enlightened
Jul
2
awarded  Nice Answer
Jul
2
comment $\mathbb{Z}$ is Euclidean domain
@Groups The answer should not omit the key step, namely why minimality of $\,r\,$ implies that $\,0\le r < |b|,\,$. Conceptually, this is because $W$ is closed under subtraction by $b$ (when $> 0),$ so if $\,r \ge |b|\,$ then $\,r > r-b\in W\,$ contra minimality of $\,r.\,$ Intuitively the induction amounts to adding or subtracting $\,b\,$ from $\,a\,$ until we land in the interval $\,[0,b)\ \ $
Jul
2
revised One-dimensional Noetherian UFD is a PID
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Jul
2
comment Can we always write $gcd(x,y)$ as $ax+by$ in UFD?
@Daniel No need to link offsite when there are proofs onsite.
Jul
1
comment In what structures does $ (-1)^2 = 1$?
See this answer on the Law of Signs. There we see that it also is true for odd functions under composition.
Jul
1
revised how can I prove negative times negative is positive.
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Jul
1
revised Irreducible in $\mathbb{Z}[\sqrt{-5}]$
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Jul
1
comment prove that $\dfrac{\left( 5^{125}-1\right)}{\left( 5^{25}-1\right)}$ is composite number
This is a special case of a general class of factorizations - see my answer.
Jul
1
answered prove that $\dfrac{\left( 5^{125}-1\right)}{\left( 5^{25}-1\right)}$ is composite number
Jul
1
comment Least Common Denominator: $ \frac{\sqrt{x}}{x}+\frac{\ln\ x}{2\sqrt{x}} $
Hint: $\ \color{#c00}{x = \sqrt{x}^{\,\large 2}}\ $ so $\, \dfrac{\sqrt x}{\color{#c00}x} = \dfrac{\sqrt x}{\color{#c00}{\sqrt{x}^{\,\large 2}}} = \,\ldots\ $ by cancelling $\,\sqrt x\ \ $
Jun
30
reviewed Close How to make a $4 \times 6$ matrix from a $6 \times 6$ diagonal matrix in MATLAB
Jun
30
revised How to show this fraction is not an integer
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