求方程 x4- y4=n　 ( n∈ N)的整数解 ,至今还没见到一般方法 ,本文将给出这类不定方程一种解法 .文中字母 P表示质数集 ,符号 ( a,b)( a、b∈ Z)表示不定方程　　 x4- y4=n　 ( n∈ N) ( 1 )的整数解 .定理 1　若 n∈ P,则方程 ( 1 )没有整数解 .证明　假定方程 ( 1 )有整数解 For the integer solution of the equation x4- y4=n (n∈ N), we haven’t seen the general method so far. This paper will give a solution to this kind of indefinite equation. The letter P in the text represents the prime number set, symbol (a, b) ( a, b ∈ Z) represents the integer solution of the indefinite equation x4- y4=n ( n∈ N) (1). Theorem 1 If n ∈ P, then equation (1) has no integer solution. Proof Assume that equation (1) has an integer solution