Homework Answers
HomeworkLib
policy first question only unless specifically stated otherwise
For Exercises 1-15, prove or disprove the given statement. 1. The product of any three consecutive...
For Exercises 1-15, prove or disprove the given
statement.
1. The product of any three consecutive integers is even.
2. The sum of any three consecutive integers is
even.
3. The product of an integer and its square is
even.
4. The sum of an integer and its cube is even.
5. Any positive integer can be written as the sum of
the squares of two integers.
6. For a positive integer
7. For every prime number n, n +...
please answer questions #7-13 7. Use a direct proof to show every odd integer is the...
please answer questions #7-13
7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers...
1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers na +3n+6 and n2 + 2n +7 cannot be prime at the same time. (b) Find 15261527863698656776712345678%5 without using a calculator. (c) Let a be an integer number. Suppose a%2 = 1. Find all possible values of (4a +1)%6. 2. (Integers: %, =) (a) Suppose a, b, n are integer numbers and n > 0. Prove that (a+b)%n = (a%n +B%n)%n. (b) Let a,...
1) Prove for any integer n, if n2 is a multiple of 6 then so is...
1) Prove for any integer n, if n2 is a multiple of 6 then so is n. To get credit, you should use the following facts in your proof: If n2 is even then so is n. (Proved) If n2 is a multiple of 3, then so is n. (Proved) 2)By contradiction, prove that the square root of 6 is irrational. The result of part 1 should be be used as Lemma in your proof.
4.3. Let p 2 3 be a prime, and let m 2 1 be an integer...
4.3. Let p 2 3 be a prime, and let m 2 1 be an integer that is relatively prime to p 1. (a) Prove that the map to itself. (b) Prove that the equation is an isomorphism of F has exactly p 1 projective solutions with x, y,zEF
Prove that if an integer n is not divisible by 3, then n^2=3k+1 for some integer...
Prove that if an integer n is not divisible by 3, then n^2=3k+1 for some integer k. Note: “not divisible by 3” means either “n=3m+1 for some integer m” or “n=3m+2 for some integer m”.
IN PYHTON CODE Question #3 Produce a function prime_factors.dict that has one integer variable n that...
IN PYHTON CODE
Question #3 Produce a function prime_factors.dict that has one integer variable n that is assumed to be greater than 1. The function will return a dictionary with keys the integers from 2 to n, inclusive, and with values the set of prime factors of each key. So, the command prime_factors.dict (8) will return the dictionary 2 123,3: 3),4 2),5 (53,6 2,3),7:7),8 {2)) Note that even though the prime number 2 appears twice in the prime fac- torization...
3) Prove the expression (p – 1)(p − 2)(p – 3) ... (p – k). -;...
3) Prove the expression (p – 1)(p − 2)(p – 3) ... (p – k). -; where k sp - 2, k a whole number. (k + 1)! is an integer whenever p is prime greater than 2.
Prove/disprove with mathematical induction that for any positive integer, n: In text form: 1 + 2...
Prove/disprove with mathematical induction that for any positive
integer, n:
In text form:
1 + 2 + . . . + n = (n*(n+1))/2
Please provide actual answer instead of a link to an answer that
is incorrect...
proofs For this assignment, know that: An integer is any countable number. Examples are: -3, 0,...
proofs For this assignment, know that: An integer is any countable number. Examples are: -3, 0, 5, 1337, etc. A rational number is any number that can be written in the form a/b, a and b are integers in lowest terms, and b cannot equal 0. Examples are 27, 22/7, -3921/2, etc. A real number is any number that is not imaginary or infinity. Examples are 0, 4/3, square root of 2, pi, etc. 1. Prove or disprove: There exists...
For Exercises 1-15, prove or disprove the given
statement.
1. The product of any three consecutive integers is even.
2. The sum of any three consecutive integers is
even.
3. The product of an integer and its square is
even.
4. The sum of an integer and its cube is even.
5. Any positive integer can be written as the sum of
the squares of two integers.
6. For a positive integer
7. For every prime number n, n +...
please answer questions #7-13
7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
1. (Integers: primes, divisibility, parity.) (a) Let n be a positive integer. Prove that two numbers na +3n+6 and n2 + 2n +7 cannot be prime at the same time. (b) Find 15261527863698656776712345678%5 without using a calculator. (c) Let a be an integer number. Suppose a%2 = 1. Find all possible values of (4a +1)%6. 2. (Integers: %, =) (a) Suppose a, b, n are integer numbers and n > 0. Prove that (a+b)%n = (a%n +B%n)%n. (b) Let a,...
4.3. Let p 2 3 be a prime, and let m 2 1 be an integer that is relatively prime to p 1. (a) Prove that the map to itself. (b) Prove that the equation is an isomorphism of F has exactly p 1 projective solutions with x, y,zEF
IN PYHTON CODE
Question #3 Produce a function prime_factors.dict that has one integer variable n that is assumed to be greater than 1. The function will return a dictionary with keys the integers from 2 to n, inclusive, and with values the set of prime factors of each key. So, the command prime_factors.dict (8) will return the dictionary 2 123,3: 3),4 2),5 (53,6 2,3),7:7),8 {2)) Note that even though the prime number 2 appears twice in the prime fac- torization...
3) Prove the expression (p – 1)(p − 2)(p – 3) ... (p – k). -; where k sp - 2, k a whole number. (k + 1)! is an integer whenever p is prime greater than 2.
Prove/disprove with mathematical induction that for any positive
integer, n:
In text form:
1 + 2 + . . . + n = (n*(n+1))/2
Please provide actual answer instead of a link to an answer that
is incorrect...
Most questions answered within 3 hours.
-
Romeo wishes to throw a bouquet of flowers to Juliet, who is on
a second-story balcony,...
asked 14 minutes ago -
Why is QE a controversial monetary policy tool.
A. It may lead to excessive inflation.B. By...
asked 30 minutes ago -
A finite potential well has depth U0 = 2.78 eV . What is the
penetration distance...
asked 56 minutes ago -
1. The bus bars of a power station are in two sections A and B
separated...
asked 55 minutes ago -
Fiscal policy is the deliberate manipulation of taxes and
government spending to alter GDP, employment, inflation...
asked 1 hour ago -
evaluating an expression using only one digit and + and - as
operators ....3+5-1+7-5+8
-----------------------
stack...
asked 1 hour ago -
Two concentric current loops lie in the same plane. The smaller
loop has a radius of...
asked 2 hours ago -
1)Which of the following is an
important difference between qualified and nonqualified retirement
plans?
a. Qualified...
asked 2 hours ago -
What's the streaming business's problem on the
horizon?
asked 3 hours ago -
I need help with writing the conclusion for this online lab
report
Abstract
By testing the...
asked 3 hours ago -
For the reaction 1N2+3H2-----> 2NH3, would the reaction rate
trend be: delta[NH3]/ delta t = -2...
asked 4 hours ago -
Within your current/past organization, identify a problem/issue
and format a design to address same. You may...
asked 3 hours ago