Use induction to prove that 8^n - 3^n is divisible by 5 for all integers n>=1.

Expert Solution

Colby Messinger answered 1 year ago

Prove by induction that 14^n + 12^n −5^n is divisible by 7 for all n >0

Use double induction to prove that (m+ 1)^n> mn for all positive integers m; n

a) Prove by induction that if a product of n polynomials is divisible by an irreducible...

a) Prove by induction that if a product of n polynomials is divisible by an irreducible polynomial p(x) then at least one of them is divisible by p(x). You can assume without a proof that this fact is true for two polynomials. b) Give an example of three polynomials a(x), b(x) and c(x), such that c(x) divides a(x) ·b(x), but c(x) does not divide neither a(x) nor b(x).

Use induction to prove that for any positive integer n, 8^n - 3^n is a multiple...

Use induction to prove that for any positive integer n, 8^n - 3^n is a multiple of 5.

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2)...

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2) Prove that a finite set with n elements has 2n subsets (3) Prove that every amount of postage of 12 cents or more can be formed using just 4-cent and 5-cent stamps

Use a mathematical induction for Prove a^(2n-1) + b^(2n-1) is divisible by a + b, for...

Use a mathematical induction for Prove a^(2n-1) + b^(2n-1) is divisible by a + b, for n is a positive integer

5. Without using the method of mathematical induction, prove that 5^n − 3^n + 2n is...

5. Without using the method of mathematical induction, prove that 5^n − 3^n + 2n is divisible by 4 for all natural n.

12 pts) Use Mathematical Induction to prove that an=n3+5n is divisible by 6 when ever n≥0....

12 pts) Use Mathematical Induction to prove that an=n3+5n is divisible by 6 when ever n≥0. You may explicitly use without proof the fact that the product n(n+1) of consecutive integers n and n+1 is always even, that is, you must state where you use this fact in your proof.Write in complete sentences since this is an induction proof and not just a calculation. Hint:Look up Pascal’s triangle. (a) Verify the initial case n= 0. (b) State the induction hypothesis....

prove that the square of the product of 3 consecutive integers is always divisible by 12

Prove that for all integers n ≥ 2, the number p(n) − p(n − 1) is...

Prove that for all integers n ≥ 2, the number p(n) − p(n − 1) is equal to the number of partitions of n in which the two largest parts are equal.

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