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The essence of mathematics lies precisely in its freedom. - Georg Cantor

Once you have tasted flight in mathematical skies, you will forever walk the Earth with your eyes turned skyward, for there you have been, and there you will always long to return.


8h
reviewed Leave Open How can you proof that the sum of three roots is irrational?
9h
comment Congruence classes -finding the order
Why do you think that the additive order is infinity?
11h
comment Multiplicative inverses and co-primes
@BSchlinker One can also view it is terms of divisibility mod $\,n,\,$ namely, notice that $\ ax\equiv b\pmod n\,$ is solvable $\iff a\mid b\pmod n\iff (a,n)\mid b,\,$ see this answer.
11h
revised Comaximal ideals
added 34 characters in body
12h
comment Multiplicative inverses and co-primes
@BSchlinker More generally, using essentially the same method, one can show $\ ax\equiv b\pmod n\ $ has a solution $\,x\iff \gcd(a,n)\mid b.\,$ Yours is the special case $\,b = 1.\ \ $
12h
comment Multiplicative inverses and co-primes
@BSchlinker The proof shows that the only (positive) common divisor of $\,a,n\,$ is $\,d = 1.\,$ Therefore, in particular, their greatest common divisor is $\, 1.\ \ $
13h
answered Multiplicative inverses and co-primes
15h
comment prove that $3$ does not divide $n^2+1$
@Anant Yes, typo fixed, thanks again.
15h
revised prove that $3$ does not divide $n^2+1$
deleted 1 character in body
15h
comment How to apply a division algorithm
Does the problem state that you should use the division algorithm, or is that your guess? What is your goal?
15h
revised How to apply a division algorithm
edited tags
16h
comment Is this proof rigorus?
The argument in Proof $1$ is not complete since you have not deduced the desired result from the hypotheses. Rather, you deduced only that $\,a\nmid b\,$ (and you overlooked your case $\,a=1).\ \ $
17h
reviewed Leave Open Ring of Convergent Power Series in R and C is a Local Ring
22h
awarded  Announcer
1d
answered mutliplicative inverse
1d
comment mutliplicative inverse
Generally the simplest way is to use the version of the extended Euclidean algorithm described in this answer.
1d
comment prove that $3$ does not divide $n^2+1$
How can the OP prove that if the simpler case is troublesome?
1d
answered prove that $3$ does not divide $n^2+1$
1d
reviewed Leave Open prove that the number $38^n+31$ is composite
1d
reviewed Leave Open if the role of a numeral system is to provide a mathematical notation for representing numbers. Then how do notation less numbers look like?