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1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 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.
the cost of paint used in a redecorating job is $65.70 .This is a reduction from its original cost of $82.13 .What is the percent decrease in the cost of paint to the nearest perce
Calculate 50%
(a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is called a duad. List the 15 duads. (b) There are 15 ways to partition {1, ......, 6 } into 3 duads, such as { {1; 2}, {3, 4},
I need to follow the pattern .125,.25,.375,.5, ?
Derivatives of Exponential and Logarithm Functions : The next set of functions which we desire to take a look at are exponential & logarithm functions. The most common exponentia
If OA = OB = 14cm, ∠AOB=90 o , find the area of shaded region. (Ans:21cm 2 ) Ans: Area of the shaded region = Area of ? AOB - Area of Semi Circle = 1/2 x 14 x
The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(
Specified a system of equations, (1), we will have one of the three probabilities for the number of solutions. 1. No solution. 2. Accurately one solution. 3. Infinit
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