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We find some necessary conditions for the existence of regular p-ary bent functions (from Z n p to Zp), where p is a prime. In more detail, we show that there is no regular p-ary bent function f in n variables with w(M f ) larger than n/2, and for a given nonnegative integer k, there is no regular p-ary bent function f in n variables with w(M f )=n/2-k ( n+3/2-k, respectively) for an even n ≥ N p,k (an odd n ≥ N p,k , respectively), where N p,k is some positive integer, which is explicitly determined and the w(M f ) of a p-ary function f is some value related to the power of each monomial of f. For the proof of our main results, we use some properties of regular p-ary bent functions, such as the MacWilliams duality, which is proved to hold for regular p-ary bent functions in this paper.