Find the number of positive integers which divide 100^999 but not 100^998
Find the number of positive integers which divide 100^999 but not 100^998
khush patil , 7 Years ago
Grade 12
Algebra> Find the number of positive integers whic...
2 Answers
Arun
Let d(n) be the number of positive integers that divide n.
The following statements are true.
1. If GCD(m,n) = 1, then d(m n) = d(m) d(n).
2. If p is a prime number, then d(p^n) = n+1
So you want to compute
d(10^999) - d(10^998) =
d(2^999) d(5^999) - d(2^998) d(5^998) =
1000^2 - 999^2 =
(1000 - 999) (1000 + 999) =
1999
The following statements are true.
1. If GCD(m,n) = 1, then d(m n) = d(m) d(n).
2. If p is a prime number, then d(p^n) = n+1
So you want to compute
d(10^999) - d(10^998) =
d(2^999) d(5^999) - d(2^998) d(5^998) =
1000^2 - 999^2 =
(1000 - 999) (1000 + 999) =
1999
Aman
Let d(n) be the number of positive integers that divide n.
The following statements are true.
1. If GCD(m,n) = 1, then d(m n) = d(m) d(n).
2. If p is a prime number, then d(p^n) = n+1
So you want to compute
d(10^999) - d(10^998) =
d(2^999) d(5^999) - d(2^998) d(5^998) =
1000^2 - 999^2 =
(1000 - 999) (1000 + 999) =
1999
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