(2-1)(2+1)(2²+1)(2的4次方+1)(2的8次方+1)(2的16次方)(2的32次方+1)的个位

3个回答

  • (2-1)(2+1)(2^2 + 1)(2^4 +1)(2^8 + 1)(2^16 + 1)(2^32 + 1)

    =(2^2 -1) (2^2 + 1) (2^4 + 1) (2^8 + 1) (2^16 + 1) (2^32 + 1)

    =(2^4 -1) (2^4 + 1) (2^8 + 1) (2^16 + 1) (2^32 + 1)

    =2^64 -1

    2^1 2^2 2^3 2^4 2^5 2^6 2^7 2^8.2^64

    2 4 8 16 32 64 128 256.,...6

    2的n次方,当n为为4的整数倍时,2^n的个位数为6

    64/4 = 8,所以 2^64 的个位数为 6

    2^64 - 1 的个位数为 5