连续四个整除相乘加1是完全平方数

a(a+1)(a+2)(a+3)+1=[a(a+3)][(a+1)(a+2)]+1=(a²+3a)[(a²+3a)+2]+1=(a²+3a)²+2(a²

设其中最小的数是x,则其余三个数是x+1,x+2,x+3则x(x+1)(x+2)(x+3)+1=(x^2+3x)(x^2+3x+2)+1设x^2+3x=a则原式=a(a+2)+1=a^2+2a+1=(

设四个连续整数为n,n+1,n+2,n+3n*(n+1)*(n+2)*(n+3)+1=n*(n+3)*(n+1)*(n+2)+1=(n^2+3n)(n^2+3n+2)+1=(n^2+3n)[(n^2+

设自然数分别为n,n+1,n+2,n+3所以n(n+1)(n+2)(n+3)+1＝(n^2+3n)(n^2+3n+2)+1＝(n^2+3n)^2+2(n^2+3n)+1＝（n^2+3n+1）^2,所以

证明,4个连续自然数的积加1的和是一个奇数的平方设:4个数分别是a,a+1,a+2,a+3因为a*(a+1)(a+2)(a+3)+1=a(a+3)(a+2)(a+1)+1=(a^+3a)(a^+3a+

设四个连续的自然数为n,n＋1,n＋2,n＋3(其中n表示自然数)．依题意,得n(n+1)(n+2)(n+3)+1=[n(n+3)][(n+1)(n+2)]+1=(n2+3n)(n2+3n+2)+1=

设四个连续整数是a-1,a,a+1,a+2那么(a-1)a(a+1)(a+2)+1=[(a-1)(a+2)][a(a+1)]+1=[(a²+a)-2](a²+a)+1=(a&sup

证明：可设这4个连续整数依次为n、n+1、n+2、n+3,则有n(n+1)(n+2)(n+3)+1=n(n+3)(n+1)(n+2)+1=(n^2+3n)(n^2+3n+2)+1=(n^2+3n)^2

证明：可设这4个连续整数依次为n、n+1、n+2、n+3,则有n(n+1)(n+2)(n+3)+1=n(n+3)(n+1)(n+2)+1=(n^2+3n)(n^2+3n+2)+1=(n^2+3n)^2

设其中最小的数是x,则其余三个数是x+1,x+2,x+3则x(x+1)(x+2)(x+3)+1=(x2+3x)(x2+3x+2)+1设x2+3x=a则原式=a(a+2)+1=a2+2a+1=(a+1)

1）n(n+1)(n+2)(n+3)+1=n(n+3)(n+1)(n+2)+1=(n^2+3n)(n^2+3n+2)+1=(n^2+3n)^2+2(n^2+3n)+1=(n^2+3n+1)^2所以,四

设连续四个自然数为n,(n+1),(n+2),(n+3)n(n+1)(n+2)(n+3)+1=(n^2+3n)(n^2+3n+2)+1=(n^2+3n)^2+2(n^2+3n)+1=(n^2+3n+1

设这4个连续整数为n、n+1、n+2、n+3,则有n(n+1)(n+2)(n+3)+1=n(n+3)(n+1)(n+2)+1=(n^2+3n)(n^2+3n+2)+1=(n^2+3n)^2+2(n^2

(1)81^7-27^6-9^13=9^14-9^9-9^13=9^9(9^5-1-9^4)9^9能被9整除,因此81^7-27^6-9^13能被9整除.9^5个位数为9,9^4个位数为19^5-1-

x(x+1)(x+2)(x+3)+1=x^4+6x^3+11x^2+6x+1=x^4+6x^3+9x^2+2x^2+6x+1=x^2(x+3)^2+2x(x+3)+1=[x(x+3)+]^2是一个平方

1.(n-2)*(n-1)*n*(n+1)+1=n^4-2n^3-n^2+2n+1=n^4-2n^2(n+1)+(n+1)^2=[n^2-(n+1)]^22.设X=2003,则2001=x-2,200

n(n+1)(n+2)(n+3)+1=(n^2+3n+1)^2

你可以设这四个数为n,(n+1),(n+2),(n+3)n(n+1)(n+2)(n+3)+1=(n^2+3n)(n^2+3n+2)+1=(n^2+3n)^2+2(n^2+3n)+1=(n^2+3n+1

证明：设四个连续整数是a,a+1,a+2,a+3a（a+1)(a+2）（a+3）+1=（a+3a）（a+3a+2）+1=（a+3a）+2（a+3a）+1=（a+3a+1）证毕

设这四个连续的自然数分别为x、x＋1、x＋2、x＋3则x(x+1)(x+2)(x+3)+1=[x(x+3)][(x+1)(x+2)]+1=(x^2+3x)(x^2+3x+2)+1=(x^2+3x)^2