Mathematics Weekly Newsletter
Mathematics Weekly Newsletter

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)  
asked by lino 33 votes
answered by David Collier 46 votes

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)  
asked by JDH 24 votes
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)  
asked by Tyg13 21 votes
answered by user24142 34 votes

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)  
asked by William Stagner 21 votes

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)  
asked by coffeemath 19 votes
answered by Derek Holt 10 votes

Why does (1/3) mod 3016 = 2011?

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)  
asked by Australia 5 votes

The difference between the ring version and module version of Chinese Remainder Thereom.

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 $IJ = I \cap J$, ...

(abstract-algebra) (ring-theory) (modules) (ideals) (chinese-remainder-theorem)  
asked by Aha 7 votes
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