G. Paseman
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A motto which is related (and sometimes true) is "proofs are finite". In most systems of logic under consideration, the statement and a proof of the statement are finite strings of symbols. One can ...

Here is another way to look at the inequality. Pick the larger of $a^n$ and $b^n$ and divide through by that quantity. This reduces the problem to showing that $(1+r)^n \ge 1 + r^n$ for some ...

Galois connections are further reaching than one first realizes. One small application is in model theory, where the relation R between sentences of a theory and models given by t R M if sentence t ...

If there were no repeats, what would the degree sequence look like? Why could it not look like that?

Here is a non-answer which may prove interesting and tractable. Given a configuration of rectangles that properly tile a surrounding rectangle, one can represent the tiling in a number of ways. Two ...

If each function has a smallest period, and otherwise fits the conditions, then a proof may be forthcoming by attempting to compute the smallest period of the sum and failing. However, things become ...

Three related points are worthy of mention, showing that epsilon can be close to n. There is a result of Finsler that approximates how many primes lie between n and 2n, which is of order o(n/log(n)) ...

If you have the Euclidean distance d between the two points, and set D = the diameter of the sphere (so D = 2R), then the great circle distance is D*InvSin(d/D), where InvSin is the inverse sine ...

Here are some suggestions to approximate the limit. Consider F(n) to be the greater of 1 and the highest power of 2 that appears in the prime factorization of n. Show what the limit of the average ...

A similar problem is known in mathematics. It is called the "Postage-Stamp" problem, and usually asks which postal values can be realized and which cannot. Dynamic programming is a common but not ...

This is an example of a Constraint Satisfaction Problem. If you have more objects than bins, you can sometimes treat the bins individually (as a poster did with the case of one bin) and multiply the ...

This sounds similar to computing the last nonzero base-10 digit of factorial(n). The fact that you are, according to some scheme, dropping the last bit of what would otherwise be a Fibonacci sequence ...

It will need something clever. For $n + 1 = 6$, you need $6$ times the lcm of $1, 5$ and $10$ in order to get enough powers of 2 ( and 3 ). Is there a characterization of those $n + 1$ where the ...
Determining a nice form for $A(n)$ is a good start. This is $S(n) - S(n-1) = 2n + 2$. Now the desired sum is \begin{equation*} \sum_{k= 1}^{10} A(2k-1) = \sum_{k=1}^{10} 4k = 4 \ast 10 \ast 11 / 2 ...