Lington-Lehmer criterion in the special case of Proth's corollary to prove the primality of 353.
lemma 13
Corollry 12(Sequential ceriterion of a closed set) Let (M. Corollary 12 (Sequential criterion of a closed set) Let (M,d) be a met- ric space. A set S C M is closed if and only if for every sequence (xn) in S that converges in M, the limit of the sequence also belongs to S. Lemma 13 Let (an) be a sequence in (M, d). Let a M. Then, a is a limit point of (ra) if and only...
Hello, can you please solve 21.11, using the Theorem 21.13?
Thank you.
Problem 21.11. Prove the following corollary of Theorem 21.13 above. Theorem 21.13. Let A, B,C, and D be nonempty sets with AC and Bn D. Then
Problem 21.11. Prove the following corollary of Theorem 21.13 above.
Theorem 21.13. Let A, B,C, and D be nonempty sets with AC and Bn D. Then
Prove the following corollary:
if !lDkf(x + th)|| 〈 M for all t E [0,1], then the remainder Rk is bounded by klly S k!
Corollary 8. For any pair of feasible solutions of dual canonical linear programming problems, we have 14. State and prove the analogue of Corollary 8 for dual noncanonical linear programming problems.
Discrete Math A Criterion for Divisibility by 3. Prove that a number is divisible by 3 if the sum of its digits (when written in base 10) is divisible by 3. Again, it will help to remember what decimal notation means.
Use the Eisenstein Criterion to prove that if
is a squarefree integer, then
is irreducible in
for every
. Conclude that there are irreducible polynomials in
of every degree
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#4
(4) Use the Box-sum criterion to prove that if f is integrable on [a, b] and is also integrable on |b,e, then f is integrable on la, e) and Je fdr- o fdz+ (5) Suppose that (r) 2 0 and is continuous on a, b). Prove that if f - 0, then f(x) = 0 for all x E a,b]. Hint: Assume to the contrary that there is some r E [a, b] where f(x) > 0. What can...
Let n be a nonnegative integer and let F 22 + 1 be a Fermat number. Prove that if 3 od F., then F, is a prime number. (Note: This yields a primality test known as Pepin's Test.)
Let n be a nonnegative integer and let F 22 + 1 be a Fermat number.
Prove that if 3 od F., then F, is a prime number. (Note: This yields a primality test known as Pepin's Test.)
Consider the special case of binomial distribution such that the
probability of exactly k 'success' is given by:
. Prove that the most probable number is the the integer
such that
. In other words,
is the largest where
ranges from 0 to r.
In the case of disparate impact employment discrimination, a job criterion that seems neutral on its face may adversely impact a class. Which of the following could lead to a claim of disparate impact discrimination?