1.Department of Mathematics and Physics， Luoyang Institute of Science and Technology， Luoyang， Henan 471022， China；2.Department of Mathematics， Shanghai Normal University，Shanghai 200234， China；3.Department of Mathematics， Luoyang Normal College， Luoyang， Henan 471934， China
Abstract：Harmonic numbers Hk＝/j(k＝0,1,2,3…) play important roles in mathematics. Let p〉5be a prime. We establish the following congruences：5HH≡－Bp－3－ ，5H≡－pBp－3－p＋ ，where B0，B1，B2，… are Bernoulli numbers given byB0＝1 and Bk＝0 (n＝1,2,3，…).
2020, Vol. 54 
