Create a mathematical proof to prove the following: Given an integer n, and a list of...

Create a mathematical proof to prove the following:

Given an integer n, and a list of integers such that the numbers in the list sum up to n. Prove that the product of a list of numbers is maximized when all the numbers in that list are 3's, except for one of the numbers being either a 2 or 4, depending on the remainder of n when divided by 3.

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milcah answered 1 year ago

Prove that the proof by mathematical induction and the proof by strong induction are equivalent

Use a direct proof to prove that 6 divides (n^3)-n whenever n is a non-negative integer.

Use mathematical induction to prove that for every integer n >=2, if a set S has...

Use mathematical induction to prove that for every integer n >=2, if a set S has n elements, then the number of subsets of S with an even number of elements equals the number of subsets of S with an odd number of elements. pleases send all detail solution.

Use mathematical induction to prove that for each integer n ≥ 4, 5n ≥ 22n+1 +...

Use mathematical induction to prove that for each integer n ≥ 4, 5n ≥ 22n+1 + 100.

Prove the following theorem. If n is a positive integer such that n ≡ 2 (mod...

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Which of the following integer examples provides a proof of the existential statement "∃n ∈ ℤ,...

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Let n be a positive integer. Prove that if n is composite, then n has a...

Let n be a positive integer. Prove that if n is composite, then n has a prime factor less than or equal to sqrt(n) . (Hint: first show that n has a factor less than or equal to sqrt(n) )

For a given integer n > 1, list all primes not exceeding n. Example: n=10, output:...

For a given integer n > 1, list all primes not exceeding n. Example: n=10, output: 2,3,5,7 n=16, output: 2,3,5,7,11,13 In Java please

a. Use mathematical induction to prove that for any positive integer ?, 3 divide ?^3 +...

a. Use mathematical induction to prove that for any positive integer ?, 3 divide ?^3 + 2? (leaving no remainder). Hint: you may want to use the formula: (? + ?)^3= ?^3 + 3?^2 * b + 3??^2 + ?^3. b. Use strong induction to prove that any positive integer ? (? ≥ 2) can be written as a product of primes.

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