This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether ce...This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.展开更多
Let d^(∗)_(k)(x)be the most likely common differences of arithmetic progressions of length k+1 among primes≤x.Based on the truth of Hardy–Littlewood Conjecture,we obtain that lim x→+∞d^(∗)_(k)(x)(x)=+∞uniformly i...Let d^(∗)_(k)(x)be the most likely common differences of arithmetic progressions of length k+1 among primes≤x.Based on the truth of Hardy–Littlewood Conjecture,we obtain that lim x→+∞d^(∗)_(k)(x)(x)=+∞uniformly in k,and every prime divides all sufficiently large most likely common differences.展开更多
Against the backdrop of all-time low relations with Asian neighbors, Japan's Emperor Akihito used the occasions of his annual birthday press conference and New Year greeting to talk to his nation about wartime his...Against the backdrop of all-time low relations with Asian neighbors, Japan's Emperor Akihito used the occasions of his annual birthday press conference and New Year greeting to talk to his nation about wartime history. The fact that he rarely addresses展开更多
基金supported by a National Key Basic Research Project of ChinaNSFC
文摘This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.
文摘Let d^(∗)_(k)(x)be the most likely common differences of arithmetic progressions of length k+1 among primes≤x.Based on the truth of Hardy–Littlewood Conjecture,we obtain that lim x→+∞d^(∗)_(k)(x)(x)=+∞uniformly in k,and every prime divides all sufficiently large most likely common differences.
文摘Against the backdrop of all-time low relations with Asian neighbors, Japan's Emperor Akihito used the occasions of his annual birthday press conference and New Year greeting to talk to his nation about wartime history. The fact that he rarely addresses
