设这四个连续自然数为：m、(m+1)、(m+2)、(m+3).依题意即：m(m+1)(m+2)(m+3)+1 =[m(m+3)][(m+1)(m+2)]+1 =[m^2+3m][m^2+3m+2]+1 =[m^2+3m]^2+2[m^2+3m]+1 =[m^2+3m+1]^2 =[m(m+3)+1]^2所以必然是一个奇数的平方....