In this paper,we prove two supercongruences conjectured by Z.-W.Sun via the Wilf-Zeilberger method.One of them is,for any prime p>3,4F3[7/6 1/2 1/2 1/2 1/6 1 1]-1/8]-1/2≡p(-2/p)+p^(3)/4(2/p)Ep-3 (mod p^(4))where(&...In this paper,we prove two supercongruences conjectured by Z.-W.Sun via the Wilf-Zeilberger method.One of them is,for any prime p>3,4F3[7/6 1/2 1/2 1/2 1/6 1 1]-1/8]-1/2≡p(-2/p)+p^(3)/4(2/p)Ep-3 (mod p^(4))where(·/p)stands for the Legendre symbol,and E_(n)is the n-th Euler number.展开更多
In this paper,the author partly proves a supercongruence conjectured by Z.-W.Sun in 2013.Let p be an odd prime and let a∈Z^(+).Then,if p≡1(mod 3),[5/6p^(a)]∑k=0(2kk)/16^(k)≡(3/p^(a))(mod p^(2))is obtained,where(■...In this paper,the author partly proves a supercongruence conjectured by Z.-W.Sun in 2013.Let p be an odd prime and let a∈Z^(+).Then,if p≡1(mod 3),[5/6p^(a)]∑k=0(2kk)/16^(k)≡(3/p^(a))(mod p^(2))is obtained,where(■)is the Jacobi symbol.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12001288)。
文摘In this paper,we prove two supercongruences conjectured by Z.-W.Sun via the Wilf-Zeilberger method.One of them is,for any prime p>3,4F3[7/6 1/2 1/2 1/2 1/6 1 1]-1/8]-1/2≡p(-2/p)+p^(3)/4(2/p)Ep-3 (mod p^(4))where(·/p)stands for the Legendre symbol,and E_(n)is the n-th Euler number.
基金supported by the National Natural Science Foundation of China(Nos.12001288,12071208)
文摘In this paper,the author partly proves a supercongruence conjectured by Z.-W.Sun in 2013.Let p be an odd prime and let a∈Z^(+).Then,if p≡1(mod 3),[5/6p^(a)]∑k=0(2kk)/16^(k)≡(3/p^(a))(mod p^(2))is obtained,where(■)is the Jacobi symbol.
