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Dec
3
accepted Proving a property about quadratic residues
Dec
3
comment Proving a property about quadratic residues
Perfect, I knew I was missing something simple.
Dec
3
asked Proving a property about quadratic residues
Oct
7
comment Is there a discrete relationship shared between patterns and series or sequences?
For your example, to define the pattern as a sequence you might use $a(n) = a(n-1) + 2010 + 200*(n \% 2)$. There's not necessarily a reason to suggest that the next number in the sequence HAS to be +2210, but absent any other available information it's a reasonable choice for continuing the pattern. Although consider if the sequence had been instead $a(n) = a(n-1)+2010+200*(f(n))$ where $f(n)$ is the fibonacci sequence starting with the unconventional $1,0,1,1,2,...$ The initial three terms would still be identical.
Jul
2
awarded  Curious
Jun
3
answered Why do negative exponents work the way they do?
May
5
comment Non-unique prime factorisation
What happens if you replace $(6,0)=(1,1)*(1,-1)$ with $(z,z)*(z,-z)$?
Apr
30
comment Placing indistinguishable objects on a indistinguishable shelve
You have to take care here because the bookshelves are indistinguishable, therefore the permutations $\star \star \star \star \star \star \star \star \star \,\star \mid\; \mid$ and $ \mid \star \star \star \star \star \star \star \star \star \star \mid$ are indistinguishable, for example.
Apr
25
revised Partial derivatives of polynomial in two variables
added instructions on performing the partial derivative.
Apr
24
answered Partial derivatives of polynomial in two variables
Apr
24
comment Partial derivatives of polynomial in two variables
I believe that $y$ should be raised to the power $j$ in your formula, as opposed to $i$?
Apr
19
awarded  Yearling
Apr
18
comment How to know if the mth root of n is an integer?
Yes, see, for example, cr.yp.to/papers/powers.pdf
Apr
14
revised Derivative of $\; y={(1+e^x)}^{0.5}\; $ using the definition of the derivative
corrected formatting
Apr
14
suggested approved edit on Derivative of $\; y={(1+e^x)}^{0.5}\; $ using the definition of the derivative
Apr
14
comment Prove that there are two frogs in one square.
@DonAntonio - I assumed that we were supposed to wind up with two frogs per square for every square.
Apr
14
comment Prove that there are two frogs in one square.
@DonAntonio: Then there will only be a single frog on every white square, and a single black frog jumping onto the black square in front of it.
Apr
14
comment Prove that there are two frogs in one square.
This isn't about probability or combinatorics. This is related to the Hilbert Paradox of the Grand Hotel (en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel).
Apr
14
comment Easy as $3.14$ question
The first entry is $2003=2$ therefore it's more likely prime digits (and letting 1 be prime as well).
Apr
11
comment Generalizations of the golden and silver ratios, and their significance
They have less and less importance as you increase in the height. If you look at the wikipedia page on the silver ratio (en.wikipedia.org/wiki/Silver_ratio) you can find section on "silver means" that generalizes it to "metallic means" and then specifically mentions the "bronze mean".