Question

Let f(n) be a negligible function and k a positive integer. Prove the following: (a) f(√n)...

Let f(n) be a negligible function and k a positive integer. Prove the following:

(a) f(√n) is negligible.

(b) f(n/k) is negligible.

(c) f(n^(1/k)) is negligible.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Euler's Totient Function Let f(n) denote Euler's totient function; thus, for a positive integer n, f(n)...
Euler's Totient Function Let f(n) denote Euler's totient function; thus, for a positive integer n, f(n) is the number of integers less than n which are coprime to n. For a prime p its is known that f(p^k) = p^k-p^{k-1}. For example f(27) = f(3^3) = 3^3 - 3^2 = (3^2) 2=18. In addition, it is known that f(n) is multiplicative in the sense that f(ab) = f(a)f(b) whenever a and b are coprime. Lastly, one has the celebrated generalization...
let's fix a positive integer n. for a nonnegative integer k, let ak be the number...
let's fix a positive integer n. for a nonnegative integer k, let ak be the number of ways to distribute k indistinguishable balls into n distinguishable bins so that an even number of balls are placed in each bin (allowing empty bins). The generating function for sequence ak is given as 1/F(x). Find F(x).
4) Let F be a finite field. Prove that there exists an integer n ≥ 1,...
4) Let F be a finite field. Prove that there exists an integer n ≥ 1, such that n.1F = 0F . Show further that the smallest positive integer with this property is a prime number.
Let λ be a positive irrational real number. If n is a positive integer, choose by...
Let λ be a positive irrational real number. If n is a positive integer, choose by the Archimedean Property an integer k such that kλ ≤ n < (k + 1)λ. Let φ(n) = n − kλ. Prove that the set of all φ(n), n > 0, is dense in the interval [0, λ]. (Hint: Examine the proof of the density of the rationals in the reals.)
Prove let n be an integer. Then the following are equivalent. 1. n is an even...
Prove let n be an integer. Then the following are equivalent. 1. n is an even integer. 2.n=2a+2 for some integer a 3.n=2b-2 for some integer b 4.n=2c+144 for some integer c 5. n=2d+10 for some integer d
Let n be a positive odd integer, prove gcd(3n, 3n+16) = 1.
Let n be a positive odd integer, prove gcd(3n, 3n+16) = 1.
Let n ∈ N and f : [n] → [n] a function. Prove that f is...
Let n ∈ N and f : [n] → [n] a function. Prove that f is a surjection if and only if f is an injection.
. Let f : Z → N be function. a. Prove or disprove: f is not...
. Let f : Z → N be function. a. Prove or disprove: f is not strictly increasing. b. Prove or disprove: f is not strictly decreasing.
Let n be an integer, with n ≥ 2. Prove by contradiction that if n is...
Let n be an integer, with n ≥ 2. Prove by contradiction that if n is not a prime number, then n is divisible by an integer x with 1 < x ≤√n. [Note: An integer m is divisible by another integer n if there exists a third integer k such that m = nk. This is just a formal way of saying that m is divisible by n if m n is an integer.]
Discrete Math 6. Prove that for all positive integer n, there exists an even positive integer...
Discrete Math 6. Prove that for all positive integer n, there exists an even positive integer k such that n < k + 3 ≤ n + 2 . (You can use that facts without proof that even plus even is even or/and even plus odd is odd.)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT