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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).
In the view below of the robot type of Cartesian Coordinates, is not the "Z" and "Y" coordinates reversed? http://www.expertsmind.com/topic/robot-types/cartesian-coordinates-91038
-3x=-57
Q. How to Add Mixed Numbers? Ans. If you have to add mixed numbers, you might try this method first: First rewrite the mixed number as a whole number plus a fracti
2x+3y=1, 5x+7y=3.
(8-)
Ask questioOn average, Josh makes three word-processing errors per page on the first draft of his reports for work. What is the probability that on the next page he will make a) 5
Determine or find out if the following series converges or diverges. If it converges find out its value. Solution We first require the partial sums for this series.
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Illustration : Solve the following IVP. Solution: First get the eigenvalues for the system. = l 2 - 10 l+ 25 = (l- 5) 2 l 1,2 = 5 Therefore, we got a
what is a redtilinear figure? like what are for the requirments for a shape to be called that? example a regular polygon has all sides and angles equal. i cant find that kind of dr
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