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Aug
10
comment Is there a way to pick a $k$ such that $p_0p_1 + ik$ is always a product of two primes?
$p_0p_1+(p_0p_1)k = p_0p_1 (1 + k)$, no?
Jun
16
awarded  Enthusiast
Jun
11
accepted Combinatorial proof that binomial coefficients are given by alternating sums of squares?
Jun
11
comment Combinatorial proof that binomial coefficients are given by alternating sums of squares?
Very nice! (characters...)
Jun
11
asked Combinatorial proof that binomial coefficients are given by alternating sums of squares?
Feb
11
comment If a product of relatively prime integers is an $n$th power, then each is an $n$th power
Have you considered the prime factorizations of $a$, $b$, and $c$?
Feb
9
revised Can someone explain how this question is reduced using basic postulates
add info on p6b
Feb
9
answered Can someone explain how this question is reduced using basic postulates
Feb
8
comment No prime number between number and square of number
Bertrand's postulate guarantees the existence of a prime between $n$ and $2n$ for all integers $n > 1$. Therefore there are no non-trivial examples of the phenomenon you describe.
Jan
17
awarded  Nice Answer
Jan
16
awarded  Commentator
Jan
16
comment Why do we need to prove $e^{u+v} = e^ue^v$?
@bobobobo In that case, we have no a priori information about the function $e^x$, and we've got to establish its basic properties from the definition provided.
Jan
16
answered Why do we need to prove $e^{u+v} = e^ue^v$?
Jan
16
comment Why do we need to prove $e^{u+v} = e^ue^v$?
It's also quite common to define $ln(x)$ as the integral $\int_1^a \frac{1}{x} \, dx$, which might be the case here.
Jan
16
comment Why do we need to prove $e^{u+v} = e^ue^v$?
How is the function $e^x$ defined in the text?
Jan
10
awarded  Scholar
Jan
10
accepted Topic for a high school-level math elective?
Jan
10
comment Topic for a high school-level math elective?
Great info. Thanks!
Jan
10
awarded  Nice Question
Jan
8
comment Topology of the power set
@t.spero: Xiaochuan is using the product topology on $2^{[0,1]}$. (The reference to Tycohoff's theorem is a clue!) More information is available on wikipedia. In concrete terms, if your base set is $S$, open sets on $\mathcal{P}(S)$ are generated by the sets $\mathcal{U}(F, G)$ for finite sets $F$ and $G \in S$, where $\mathcal{U}(F,G)$ is defined to be $\{U \subset S : F \subset U \text{ and } G \cap U = \emptyset\}$. (I believe I have that right, but I am also tired, so no guarantees.)