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Results tagged with big-list
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user 6698
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
0
votes
Unconventional types of induction
The following induction method is almost never mentioned:
Step 1: Prove something is true for $n = i$, for $i$ with $1 \le i \le k-1$, where $k \ge 2$ may be arbitrarily chosen.
Step 2: Assuming it' …
15
votes
What are some examples of ingenious, unexpected constructions?
I think Elkies' construction of numbers $a,b,c,d$, such that $a^4 + b^4 + c^4 = d^4$, disproving Euler's sum of powers conjecture, is quite impressive. Another nice construction from number theory is …
6
votes
Contest problems with connections to deeper mathematics
A problem on Tournament of the towns 2002 Fall/A-level:
A sequence with first two terms equal to $1$ and $24$ respectively, is defined by the following rule: each subsequent term is equal to the smal …
1
vote
Theorems that are 'obvious' but hard to prove
Very good candidates for this question are theorems that amount to saying that some sequence behaves randomly in a way. Both the fact that the statements are obvious and the fact that they are usually …
15
votes
Awfully sophisticated proof for simple facts
An olympiad-type question I once tried to solve was: prove that all integers $>1$ can be written as a sum of two squarefree integers$^{[1]}$. The proof I came up with (which uses at least $3$ non-triv …