Let d be a positive integer which is square free,h(d)be the class number of thereal quadratic field.In this paper,we prove that(1)if the equation U ̄2-dV ̄2=4 hasinteger solution with(U,V )=1,then the diophantine equation 4x ̄(2n)-dy ̄2=-1,n>2 hasno solution in positive integers,except d = 5,2=y=1;(2)if the positive integers a,k,nsatisfy,n> 2 and is the fundamental solution of Pell′s equationx ̄2-dy ̄2=-1,Then h(d)≡0(mod n).