Question

(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1=?

Answer 1

原式
=[(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)]/(5-1)+1/4
=[(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)]/4+1/4
=[(5^4-1)(5^4+1)(5^8+1)(5^16+1)]/4+1/4
=[(5^8-1)(5^8+1)(5^16+1)]/4+1/4
=[(5^16-1)(5^16+1)]/4+1/4
=(5^32-1)/4+1/4
=5^32/4-1/4+1/4
=5^32/4

追问

是4分之5的32次 还是5的4分之32次啊

追答

(5^32)/4

Answer 2

(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1
=(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)/(5-1)+1
=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)/(5-1)+1
=(5^4-1)(5^4+1)(5^8+1)(5^16+1)/(5-1)+1
=(5^8-1)(5^8+1)(5^16+1)/(5-1)+1
=(5^16-1)(5^16+1)/(5-1)+1
=5^32-1/4+1
=5^32/4+3/4

Answer 3

(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1
=1/4*(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1
=1/4*(5²-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1
=1/4*(5^4-1)(5^4+1)(5^8+1)(5^16+1)+1
=1/4*(5^8-1)(5^8+1)(5^16+1)+1
=1/4*(5^16-1)(5^16+1)+1
=1/4*(5^32-1)+1
=1/4 *5^32-1/4+1
=(5^32 + 3)/4

Answer 4

设：A=﹙5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
∴4A=﹙5－1﹚﹙5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
4A=(5^2－1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
4A=(5^4－1)(5^4+1)(5^8+1)(5^16+1)
4A=(5^8－1)(5^8+1)(5^16+1)
4A=5^32－1
∴A=﹙5^32－1﹚／4
∴(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1=A＋1=﹙5^32＋3﹚／4

Answer 5

(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1
=(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)/(5-1)+1
=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)/(5-1)+1
=(5^4-1)(5^4+1)(5^8+1)(5^16+1)/(5-1)+1
=(5^8-1)(5^8+1)(5^16+1)/(5-1)+1
=(5^16-1)(5^16+1)/(5-1)+1
=(5^32-1)/(5-1)+1
后面就不知道了，是不是题错了？

Answer 6

(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1=[(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1]/4
=(5^32)/4