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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).
arrange these numbers in ascending order. -5 -7 1 2 15 0 - 25
in the quadrilateral abcd,ab is 4.3,bd is 5.1,ad is 4.8.angle bdc is 20 degrees and angle c is 80 degrees.all dimentions in metres.calculate the unknown sides and angles of the plo
example #Minimum 100 words accepted#
Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers
Find out the area under the parametric curve given by the following parametric equations. x = 6 (θ - sin θ) y = 6 (1 - cos θ) 0 ≤ θ ≤ 2Π Solution Firstly, notice th
Round 468.235 to the nearest hundredth ? The hundredths place is the second digit to the right of the decimal point (3). To decide how to round, you must like as at the digit t
By which of those ancient civilizations was Machu Pichu built? The Aztecs The Egyptians The Mayas The Incas Which state sold Corsica to France in 1768? - Not answered Genoa Veni
I am really stuck on this topic and other topics its extremely difficult and I dont know what to do Im stressing out help me please.
the ratio of boys to girls in the sixth grade is 2:3 if there are 24 boys, how many are girls?
Download the data on Gas Mileage. This is a sample of 81 passenger cars with information about gas consumption and other technical details. a. Estimate the following
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