Eulerʼs proof of the infinitude of primescombinatorial proofP. Erdős found numerous theorems, problems, results and conjectures in elementary number theory. Some of them are two Erdősʼs proofs of of the famous Euclidʼs theorem on the infinitude of primes. As noticed below, one of...
Standard methods from the anatomy of integers can then be used to see how dense a set with that many prime factors could be, and this soon led to a short proof of part (ii) of the main theorem (I eventually found for instance that Jensen’s inequality could be used to create a ...
211时不成立. 最后,我们还提出了一些问题和猜想供更进一步的研究和探索. 关键词极大集:素数;Erd6s猜想 Abstract Matllem撕cianErd6sdevotedhiswholelifetO posingmanyconjectures for discussing.In ourarticle,weresearchona conjecture ofErd6s.Thespecific workis asfollows: Let f(n,k)be the largest numberof...
6 Chapter2 2.1ProofofTheorem4………..6 2.2 Lemmas 2……….. 7 PreliminaryforConiecture 2.3 2for七=3……….12 Conjecture 2.4ProofofTheorem 1………..12 2.5 2 Conjecturefor后=4……….14 2.6ProofsofTheorem2and 1 for尼=4………18 Conjecture 2.7Proofs 1 and 2………..20 ofPropositions ...
Kneser conjectureKneser hypergraphChromatic numberTopological Tverberg theoremAlon, Frankl, and Lovasz proved a conjecture of Erdos that one needs at least [n-r(k-1)/r-1] colors to color the k-subsets of {1, ... , n} such that any r of the k-subsets that have the same color are ...