THE PARTIAL SUMS OF THE HARMONIC SERIES
... Therefore Hn tend to infinity at the same rate as ln n, which is fairly slow. For instance, the sum of the first million terms is H1000000 < 6 ln 10 + 1 ≈ 14.8. Consider now the differences δn = Hn − ln n. Since ln(1 + n1 ) < Hn − ln n < 1, ...
... Therefore Hn tend to infinity at the same rate as ln n, which is fairly slow. For instance, the sum of the first million terms is H1000000 < 6 ln 10 + 1 ≈ 14.8. Consider now the differences δn = Hn − ln n. Since ln(1 + n1 ) < Hn − ln n < 1, ...
Cryptology
... Selection of prime numbers. Issue 1: How to test if a large number is prime? Issue 2: probability that a large number is prime? Selection of a primitive root. Theoretical estimate: There are primitive roots < p¼ + o(1). Exhaustive search can be exponential time (O(e(¼+o(1)) ln(p))). ERH implies: Lea ...
... Selection of prime numbers. Issue 1: How to test if a large number is prime? Issue 2: probability that a large number is prime? Selection of a primitive root. Theoretical estimate: There are primitive roots < p¼ + o(1). Exhaustive search can be exponential time (O(e(¼+o(1)) ln(p))). ERH implies: Lea ...
MAT 310-F10: REVIEW FOR FINAL EXAM (1) Consider the the 3×6
... Solution: The first 3 columns of B are independent, so its column space has dimension 3, thus rank(B)=3. The second, third and fifth column of A are independent, so its column space has dimension 3, thus rank(A)=3. If B could be obtained from A by elementary row operations, then there would exist an ...
... Solution: The first 3 columns of B are independent, so its column space has dimension 3, thus rank(B)=3. The second, third and fifth column of A are independent, so its column space has dimension 3, thus rank(A)=3. If B could be obtained from A by elementary row operations, then there would exist an ...
