## Top new questions this week:

### How many scientists can survive?

Yesterday the aliens took 100 scientists from Earth as prisoners. They want to test how smart the humans are. The aliens made 101 headbands, numbered from 1 to 101. On the contest day, they throw ...

(combinatorics) (puzzle)

### A transfinite epistemic logic puzzle: what numbers did Cheryl give to Albert and Bernard?

I expect that nearly everyone here at stackexchange is by now familiar with Cheryl's birthday problem, which spawned many variant problems, including a transfinite version due to Timothy Gowers. In ...

(logic) (ordinals)
 answered by Joe and Kellen 8 votes

### Is it possible for integer square roots to add up to another?

I initially was wondering if it were possible for there to be three $x,y,z \in \mathbb{Q}$ and $\sqrt{x},\sqrt{y},\sqrt{z} \notin \mathbb{Q}$ such that $\sqrt{x} + \sqrt{y} = \sqrt{z}$. I had ...

(elementary-number-theory)

### When are two proofs "the same"?

Often, we find different proofs for certain theorems that, on the surface, seem to be very different but actually use the same fundamental ideas. For example, the topological proof of the infinitude ...

(logic) (soft-question) (proof-theory)

### Groups with "few" subgroups

If $G$ is a finite group of order $n,$ and the number of divisors of $n$ is $k,$ can $G$ have fewer than $k$ subgroups? A cyclic group $G$ of order $n$ has exactly one subgroup for each divisor of ...

(group-theory)

So I am taking a class where we are working on a cryptography section. Basically, the course says that: $$\frac 1 3 \mod(3016) = 2011$$ or when run through Python - modified with SciPi: $$\frac 1 3 ... (elementary-number-theory) (modular-arithmetic) (cryptography)  asked by Zack 18 votes  answered by Bill Dubuque 25 votes ### What is the geometrical difference between continuity and uniform continuity? Can we explain between ordinary continuity and Uniform Continuity difference via geometrically? What is the best way to describe the difference between these two concepts to someone else? Where the ... (real-analysis) (continuity) (uniform-continuity)  asked by Nilan 17 votes  answered by String 32 votes ## Greatest hits from previous weeks: ### Probability of 3 Heads in 10 Coin Flips What's the probability of getting 3 heads and 7 tails is one flips a fair coin 10 times. I just can't figure out how to model this correctly. (probability)  asked by Newbie1923 10 votes  answered by Ayman Hourieh 19 votes ### How do we use derivatives in our daily lives How can we use derivatives in our real lives, I know that we have a lot of formulas to find the derivatives of a function,but why do we need them ? (derivatives)  asked by rabia 1 vote  answered by Robert Israel 10 votes ## Can you answer these? ### Guessing number in set 1-100 with weighted questions. It is needed to guess number from 1 to 100. I can ask questions and get answers:"yes" or "no". For the "yes"-answer I must pay one dollar, for the "no"-answer - two dollars. How many dollars should I ... (probability-theory) (information-theory)  asked by Lex 5 votes ### How prove this systems-equation has least two postive integers solution Show that： for any k\ge 100,(k\in N^{+}), there exsit p\in N^{+}, such$$\begin{cases} a+b+c=k\\ abc=p\\ a>b>c \end{cases} has at least two postive integers solution $(a,b,c)$ ...

(contest-math) (systems-of-equations)
Chinese Remainder Theorem for Commutative Rings If $R$ is a commutative ring with $1$ and $I, J$ are ideals of $R$ that are pairwise coprime or comaximal (meaning $I + J = R$), then $IJ = I \cap J$, ...