My question is: is it possible to find pentagonal numbers which are also tetrahedral? A pentagonal number is obtained by the formula: $$P_k=\frac{1}{2}k(3k-1)$$ The equivalent formula for the tetrahedral number $T_n$ is: $$T_n=\frac{1}{6}n(n+1)(n+2)$$ So the problem is to find a $T_n=P_k$ that me...

The triangular numbers 15 and 21 have the property that both their sum and difference are triangular. There are another 4 pairs less than 1000. To complete this problem, I have done like this: To satisfy the conditions, we have to find $u$, $v$, $w$, $x$ such that $$\begin{align*} \frac{u(u+1...

I am trying to find a general formula for triangular square numbers. I have calculated some terms of the triangular-square sequence ($TS_n$): $TS_n=$1, 36, 1225, 41616, 1413721, 48024900, 1631432881, 55420693056 1882672131025, 63955431761796, 2172602007770041, 73804512832419600 I have managed t...

In posted Answers one normally finds share/ edit/ flag buttons, but for some other Answers share/edit/delete/flag buttons. What decides the extra delete button to appear ?

I'm not certain if the tag should be removed (and such questions declared off-topic), but I do feel that we need to work on quality control for these questions and answers. Compare our current laissez-faire attitude about "reference requests" to physics.SE's policy. So I don't think that referen...

What is the policy on asking for recommendations of books or resources on Physics Stack Exchange? What is a resource recommendation question? What sort of resource recommendation questions are allowed here? How should I answer a resource recommendation question? As a community member, how shoul...