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location Shoulders of Giants
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visits member for 4 years
seen 1 hour ago

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.


1h
comment What would be a prime element in the field of rational numbers?
@Modp See this answer.
11h
reviewed Leave Open How large are measurable cardinals of higher orders?
11h
reviewed Leave Open Large Cardinal Inequalities
16h
reviewed Leave Open Probability of infinite intersections
17h
comment In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
Are you aware the notions of associate and irreducible bifurcate into several inequivalent notions in rings with zero-divisors? See this answer. This may explain some of the misunderstanding here (which I only had the time to peruse quickly).
17h
answered A number system that is not unique factorization domain
18h
answered Infinitude of prime numbers
19h
revised Every irreducible polynomial of degree $m$ over $\mathbb F_p$ divides $x^{p^m}-x$
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19h
answered Every irreducible polynomial of degree $m$ over $\mathbb F_p$ divides $x^{p^m}-x$
19h
answered Count the integers between $20000$ and $30000$ that end in $39$, and end in $33$ in base $4$, and end in $37$ in base $8$
20h
revised Count the integers between $20000$ and $30000$ that end in $39$, and end in $33$ in base $4$, and end in $37$ in base $8$
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22h
comment If $a^3=e$, then $a$ has a square root.
@user1729 In my experience, most students will not grasp the essence of the matter from what little was said in the other answers. There is large pedagogical abyss between most textbooks in elementary number theory and abstract algebra. This often leads to conceptual gaps in matters like this. That's why I often elaborate on such topics - to help students overcome those ubiquitous gaps.
22h
comment If $a^3=e$, then $a$ has a square root.
The donwvotes are quite puzzling. As always, if something is not clear then please feel welcome to ask questions and I will be happy to elaborate.
22h
revised If $a^3=e$, then $a$ has a square root.
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22h
revised If $a^3=e$, then $a$ has a square root.
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23h
revised If $a^3=e$, then $a$ has a square root.
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23h
revised If $a^3=e$, then $a$ has a square root.
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23h
answered If $a^3=e$, then $a$ has a square root.
23h
revised Find the sum of the multiples of $3$ and $5$ below $709$?
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23h
answered Find the sum of the multiples of $3$ and $5$ below $709$?