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1. Suppose n ≡ 7 (mod 8). Show that n ≠ x2 + y2 + z2 for any x, y, z ε Z.
2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
3. Prove that it is always possible to make postage of exactly n cents for all n ≥ 32 using only 5 and 9 cent stamps.
4. Prove that every fourth Fibonacci number is a multiple of 3.
In other words, show that 3 | f4n ∀n ≥ 1.
5. Let bn be the sequence recursively defined by b0 = 1, b1 = 5 and, for n > 1,
bn = b[n/3]+2b[n/3]
(a) Compute b26 and b27.
(b) Guess a formula for bn when n = 3t for t ≥ 0 and then use mathematical induction to prove that your guess is correct. (Be sure to include a careful statement of what you are trying to prove).
Allan has been hired to mow the school soccer field that is 180 ft wide through 330 ft long. If his mower mows strips which are 2 feet huge, how many times must he mow across the w
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Complex numbers from the eigenvector and the eigenvalue. Example1 : Solve the following IVP. We first require the eigenvalues and eigenvectors for the given matrix.
Determine if the following series converges or diverges by using limit comparison test. Solution To make use of the limit comparison test we require to find out a seco
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument: 1. H v (~T > R) 2. Hv (E > F) 3. ~T v E 4. ~H & D / R v F INSTRUCTIONS: Con
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As1212uestion #Minimum 100 words accepted#
What is partial market equilibrium
what is market
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