I was asked to prove that 5^(2n+1) + 4^(2n+1) is divisible by 9 for all n that are positive integers. I’m not allowed to use modular arithmetic, only proof by induction. I’ve proven my base case and started my inductive step, but can’t find an algebraic truck to get the result I want.

Q: find all integers n>1 such that 1^n+2^n+.....+(n-1)^n is divisible by n.

A:

Q: Prove that 1+ 2 + 22 + 23 +. + 2" = 2n+1-1 for n 2 1. Use proof by induction.

A:

Q: (b) Use mathematical induction method to show that 품(주-)- (두-0) (주-)-(-)1 n+1 2n

A:

Q: how that in the domain of integers of the form a+bsqrt(-17) the factorization…

A: The  objective is to show that 13 is irreducible. The norm of 13 is 13=132=169 So if 13 is reducible…

Q: Add and Simplify your ans 3(2)/(8)+5(1)/(8)

A:

Q: Rationalize the denomi 20 5/10 - 7/5

A: 20510-75

Q: -

A:

Q: Is it true that (3 x EN) (x²-3x +20 is a prime)? O True False

A: Is it true that ( there exists x in N)(x^2-3x+20  is a prime ) ?   True False

Q: Write a formal induction proof (Base Case and Inductive Step) Prove by induction that…

A:

Q: Value of the 7th term in (2x + y)"?

A: Follow the procedure given below.

Q: problem is from discrete math regarding profs my strong induction. If you can’t help, no worries,…

A:

Q: Use induction to prove that 2*3^(n-1) is less than or equal to 2n choose n (picture attached)

A: We have to prove 2⋅3n−1≤2nn by using of principal of mathematical induction, where n≥0 Recall that…

Q: How can I prove by induction that 2^n + 1 is divisible by three for all odd integers

A: To apply mathematical induction to show that 2^n+1 is divisible by 3 if n is odd

Q: If x is positive, the first negative term in the expansion of (1 + x)27/5 is (a) 5th term (b) 6th…

A: Introduction :

Q: find a simple recursive definition of the sequance with general term tn=2(n-1)+7 for n>2

A:

Q: This will be (n+k-1)= 29+6-1 29 -¹1) = 34 29 = 278, 256.

A:

Q: Prove that if  n  is a positive integer, then  5 | (6^n − 1)

A:

Q: 9. (a) Using Pascal's triangle, expand and simplify (1 + 2)- (1-2.r)". (b) Using the binomial…

A:

Q: Write out the full expansion of (x + y)^7 using either binomial coefficients or Pascal’s Triangle to…

A:

Q: Add as indicated in the following exp (2)/(5(k-3))+(4)/(3(k-3))

A:

Q: What is the coefficient of (x^8)(y^12) in the expansion of (2x+3y)^20

A:

Q: 10^(n+1) + 10^(n) + 1 is divisible by 3 for all positive integer n.

A:

Q: Solve for X, show all calculation in binary number system only X = ((1110)₂-(0011)₂) (10011010)₂)…

A:

Q: rationalize

A:

Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: Find all integer solutions to 105x+343y=35 Using Magic Box | Elementary Number Theory

A:

Q: Prove by induction that 11^n - 6 is divisible by 5 for all n greater than or equal to 1

A: Mathematical Induction :It is a mathematical technique used to prove the statement is true all…

Q: Find all whole#s that leave remainder 3 upon division by 5?

A: The solution is given below:

Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's Theorem: If p is a prime and a is a positive integer and not divisible by the prime p, then…

Q: what are the first three terms in the binamial, expansion of (2a-0,5b) 1.

A: Given

Q: Can you show it the "'short" way without using Pascal's method?

A: Given expression is: x-12x-24 We try to simplify it first: x-12x-24=x-12x-14=x-1·24·x-14=16x-15

Q: For n is greater than or equal to  1, use mathematical induction to establish each of the following…

A: