First proof that infinitely many prime numbers come in pairsMathematician claims breakthrough towards solving centuries-old problem.McKee, Maggie
, … of distinct primes. in particular, this shows that there are infinitely many primes. advantages of the direct proof there are several advantages of the direct proof (proof 2) over the proof by contradiction (proof 1). first, the direct proof gives an algorithm that...
MethodsofProof（证明的方法）YangJuan yangjuan@bupt.edu.cn CollegeofComputerScience&TechnologyBeijingUniversityofPosts&Telecommunications MethodsofProof Definition:Atheorem(定理)isavalid(正确)logicalassertionwhichcanbeprovedusing othertheoremsaxioms(公理)(statementswhicharegiventobetrue)andrules...
摘要: I can proof that there are infinitely many twin primes. The twin prime counting function π2(n), which gives the number of twin primes less than or equal to n for any natural number n, is for limn→∞π2(n)= 2 C2 [π(n)]^2/n where π(n) is the prime counting fu...
Each of Thompson's groups F, T, and V has infinitely many ends relative to the groups F [0, 1/2], T [0, 1/2], and V [0, 1/2) (respectively). We can therefore simplify the proof, due to Napier and Ramachandran, that F, T, and V are not Kähler groups. Thompson's grou...
There is an obvious algorithm to decide the problem: there are only finitely many choices of assignments of vertices to colors, and we can simply check them all. In fact, there are kn of them, where n is the number of vertices of G. Unfortunately, this algorithm is not polynomial in ...
Primes in intervals of bounded length The infamous twin prime conjecture states that there are infinitely many pairs of distinct primes which differ by . Until recently this conjecture had seem... A Granville - 《Bulletin of the American Mathematical Society》 被引量: 33发表: 2015年 Sketch of ...
Our main result is that if n ≥ 2, then there are infinitely many fixpoin... W Bergweiler - 《Complex Variables Theory & Application An International Journal》 被引量: 91发表: 1991年 Using Elliptic Curves of Rank One towards the Undecidability of Hilbert's Tenth Problem over Rings of ...
Yes,thisisequivalent,becauseitisthecontrapositiveofthestatement,soproving“ifP,thenQ”isequivalenttoproving“ifnotQ,thennotP”.Goal:IfP,thenQ.(PimpliesQ)Method1:WriteassumeP,thenshowthatQlogicallyfollows.RationalNumberRisrational thereareintegersaandbsuchthatandb≠0.numeratordenominatorIs0.281arationalnumber...
Infinitely Many Almost-IsoscelesPythagorean Triples ExistWordlessly, we show that there are infinitely many Pythagorean triples with consecutive integers as legs and infinitely many Pythagorean triples with consecutive triangular numbers as legs.doi:10.4169/math.mag.89.2.103...