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May
4
answered Series behavior using the Ratio Test
May
3
awarded  Popular Question
May
2
awarded  Yearling
May
2
reviewed Approve Orthogonal circles
May
2
comment Finding all integers satisfying an equation?
Your approach via differential equation is flawed at its heart. When you write $2x^2+2xy+y^2=25$, you mean that you have two integers $x$ and $y$ for which the equation is true. In order to justify deriving both sides, the equation would have to be true for all real $x$.
May
1
comment Number of integral solutions of $\text{xyz}=3000$
2, 2, 2, 3, 5, 5 and 5.
May
1
comment Number of integral solutions of $\text{xyz}=3000$
@Tejas 3000 only has 7 (prime) factors.
Apr
30
revised What kind of vector spaces have exactly one basis?
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Apr
28
awarded  Popular Question
Apr
24
comment Cartesian product of two real sets
@Jyanluka The cartesian product of $A$ and $B$ will be an infinite set.
Apr
23
accepted Order of a polynomial in $\mathbb F_q[x]$
Apr
23
asked Order of a polynomial in $\mathbb F_q[x]$
Apr
21
awarded  Nice Answer
Apr
21
answered My dilemma about $0^0$
Apr
18
revised Prove there exists $m > 2010$ such that $f(m)$ is not prime
added 244 characters in body
Apr
18
comment Prove there exists $m > 2010$ such that $f(m)$ is not prime
@AlexM. It's simply that modulo anything, congruence is compatible with addition and multiplication. So if $x\equiv y$, then $x^k\equiv y^k$, $a_kx^k\equiv a_ky^k$, and $f(x)\equiv f(y)$.
Apr
18
answered Prove there exists $m > 2010$ such that $f(m)$ is not prime
Apr
16
answered How to Prove with Mathematical Induction $3^n > n^2$
Apr
14
comment Can abstract algebra be used to prove points are constructible?
@user54301 Oh, you're thinking of a slightly different necessary condition than I was. You need a stronger necessary condition than "A point is constructible only if it's in an extension of degree $2^n$". Namely, you need the condition "A point is constructible only if it's in a tower of extensions, each extension of which is of degree $2$". This doesn't require a more complicated proof than for the weaker condition. In fact, all the proofs I know prove the stronger condition first, but then reformulate it as the weaker condition because it's simpler.
Apr
14
comment Heuristic explanation for oscillatory behavior of first $n$ primes' multiples
$\mu a_k - k$ seems like a somewhat arbitrary function to want to plot. Is it supposed to represent something meaningful?