设M=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/10/04 22:26:04
设M=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1),求M的个位数字.
M=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^16-1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^32-1)(2^32+1)(2^64+1)(2^128+1)
=(2^64-1)(2^64+1)(2^128+1)
=(2^128-1)(2^128+1)
=2^256-1
2的1次方个位数是:2
2的2次方个位数是:4
2的3次方个位数是:8
2的4次方个位数是:6
2的5次方个位数是:2
∴2的n次方个位数是以:2、4、8、6四个数为循环的
∵256÷4=64
∴2^256的个位数是:6
∴2^256-1的个位数是:5
即:M的个位数是:5
再问: 请问能告诉我要是写过程要怎么写吗?
再答: M=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1) =(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1) =(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1) …… =2^256-1 ∵2的n次方个位数是以:2、4、8、6四个数为循环的,256÷4=64 ∴2^256的个位数是:6 ∴2^256-1的个位数是:5 这样写就行了!
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^16-1)(2^16+1)(2^32+1)(2^64+1)(2^128+1)
=(2^32-1)(2^32+1)(2^64+1)(2^128+1)
=(2^64-1)(2^64+1)(2^128+1)
=(2^128-1)(2^128+1)
=2^256-1
2的1次方个位数是:2
2的2次方个位数是:4
2的3次方个位数是:8
2的4次方个位数是:6
2的5次方个位数是:2
∴2的n次方个位数是以:2、4、8、6四个数为循环的
∵256÷4=64
∴2^256的个位数是:6
∴2^256-1的个位数是:5
即:M的个位数是:5
再问: 请问能告诉我要是写过程要怎么写吗?
再答: M=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1) =(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1) =(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)(2^128+1) …… =2^256-1 ∵2的n次方个位数是以:2、4、8、6四个数为循环的,256÷4=64 ∴2^256的个位数是:6 ∴2^256-1的个位数是:5 这样写就行了!
设m n为自然数,定义m*n=m+(m+1)+(m+2)+(m+3)+.(m+n)
设m^(2)+m-1=0.求m^(3)+2m^(2)+2004的值
设m^2+m-1=0,求m^3+2m^2+2004的值
设m平方+m=1则m立方+2m平方+2007=?
设m²+m=1,求m³+2m²+2009的值
设m²+m-1=0,求m^3+2m²+2009的值,
设m²+m-1=0,求m³+2m²+3的值
若m,n为正整数,设M=2m+1,N=2n-1
设集合a={m,2m,3m},b={x/1
设m²+n-1=0,求m³+2m²+2004的值
1)设M=a+1/a-2(2
设M=a+1/(a-2)(2