Abstract: Let n be a positive integer.J.P. Jones conjectured that if n>3 and ( 2n-1n)≡0 ( mod n 3 ), n is an odd prime. In this paper, using some elementary methods of number theory, the author proves that if n is even, there is ( 2n-1n) 0(mod n 2 ), wnich means that Jones' conjecture is true for even integers n .

Key words: binomial coefficient, congruence, Wolstenholme's theorem, inverse proposition