The Diophantine equation,as the oldest branch of nmber theory,is very rich in content.The so-called Diophantine equation refers to the equation where the number of unknowns is more than the number of equations.The integer solution of x2+4n=y11 is studied by algebraic number theory and congruence and so on.It proves that the Diophantine equation x2+4n=y11 has no integer solution when x≡1(mod 2),n≥1, and shows that the Diophantine equation x2+4n=y11(n∈{1,8,9,10})has no integer solution.So the Diophantine equation x2+4n=y11 has integer solutions if and only if n≡0,5(mod11),and (x,y)=(0,4m) when n=11m, (x,y)=(211m+5,22m+1) when n=11m+5, where m is a nonnegative integer.It implies that Conjecture 1 holds for k=11.