设m²+m+7 = n^2
那么4m^2+4m+1 + 27 = 4n^2
所以(2n)^2-(2m+1)^2 = 27
所以(2n-2m-1)(2n+2m+1) = 27 = 1*27 = 3*9
所以2n-2m-1=1,2n+2m+1=27解得n=7,m=6
或2n-2m-1=3,2n+2m+1=9解得n=3,m=1
所以满足条件的整数个数为2