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 Pundit
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Feb
29
comment Can every integer greater than 5 be written as the sum of exactly one prime and one composite?
Alternatively you can also think of it this way: there's clearly always a prime $p$ between 1 and your integer $n$, and there's a good chance that $n - p$ is not prime; so clearly the problem isn't hard. it shouldn't be hard to work out possible values of $p$ that will systematically work for all $n$.
Dec
31
comment V.I. Arnold says Russian students can't solve this problem, but American students can — why?
Am I the only one who had to look up what an "altitude" meant in this context? I've only ever seen it referred to as the "height" of a triangle, as in the usual "area = base * height / 2" formula... is this US-specific terminology or something?
Nov
10
comment Are there any situations in which L'Hopital's Rule WILL NOT work?
@JoelReyesNoche Only if said conditions are both sufficient and necessary! Strictly speaking a rule may still work outside of its prescribed conditions either because they are not strict enough, or just by sheer luck. :)
Oct
24
comment Write a formula as a sum of fractions with constant numerators
For more information about this type of transformation search for "partial fraction decomposition" on google.
Aug
26
comment Is 4 the second or third digit of pi
The most versatile approximation in my opinion is 3.14159265. Easy to remember, pronounce (314 159 265), type out, extremely accurate, but not long enough to make it weird.
Aug
19
comment What is the sheafification of the presheaf of the one point compactification?
tongue twister!
Aug
4
comment A problem in integration.
@user258250 $\frac{-1}{2} \cos(2 \pi/6) - \frac{-1}{2} \cos(0) = \frac{1}{4} = \sin^2(\pi/6) - \sin^2(0) = \frac{1}{4}$
Jun
7
comment What is the difference between necessary condition & sufficient condition?
That's right; but your second sentence contradicts this: you wrote that if A' is a sufficient condition for B then A' must exist in order for B to occur, which is not true. That's why I asked if you had a typo
Jun
7
comment What is the difference between necessary condition & sufficient condition?
Typo? "Sufficient condition A′ means that A′ must exists in order for B to occur [...]"; wouldn't that mean that one must solve the Riemann hypothesis to get accepted into a prestigious university?
Jun
3
comment Is this theorem already in existence?
I think it's usually introduced to high-schoolers when factoring quadratics with integer coefficients: you expand out the product and get them to find two integers which add up to $s$ and multiply to $p$.
May
27
comment Identification of a quadrilateral as a trapezoid, rectangle, or square
Perhaps more importantly, why did your student not produce a counterexample (e.g. by drawing on the board) after her answer had been questioned? Possibly shyness/anxiety? (apologies if someone asked this before, did not read all the comments)
May
11
comment RSA, cipher, Cryptosystem
That's right (and we disregard $C_3$ because it's not needed, you only need two ciphertexts of the same plaintext encrypted with coprime public exponents to obtain a linear combination like Todd shows - 17, 19 and 21 are pairwise coprime so you could use $C_1$ and $C_2$, or $C_2$ and $C_3$, or even $C_1$ and $C_3$)
May
11
answered RSA, cipher, Cryptosystem
May
5
comment Notation (or Name) of the function which is 0 at x=0 and 1 otherwise
This isn't "traditional notation" (nor simpler) like the question asked, it seems more like obfuscation than anything.... unless this definition from the Heaviside function allows one to derive nontrivial information about the function, it seems pointless.
May
4
comment Result of solving an unsolved problem?
puts tin foil hat on maybe the NSA has already found a constructive proof that P = NP... (just kidding, or am I?)
Apr
27
accepted A quadratic polynomial bounded by another
Apr
27
comment A quadratic polynomial bounded by another
Thanks, I guess this settles it haha
Apr
27
asked A quadratic polynomial bounded by another
Apr
21
comment Determine if the following is surjective
Just wondering, how come you used a greek eta symbol rather than a plain n? Not criticising, just curious if it has any special significance...
Apr
20
comment How many scientists can survive?
"hopefully clever enough" if they aren't, the 99 scientists die in confusion while the first one dies in vain.