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1. Show that there do not exist integers x and y for which 110x + 315y = 12.
2. If a and b are odd integers, prove that a2 +b2 is divisible by 2 but is NOT divisible by 4. Hint:
Any odd number can be written 2k + 1 for some integer k.
3. Prove that for any prime number p, √ p is irrational. Hint: Follow the same method that was used to prove √ 2 is irrational, by first supposing √ p can be expressed as a=b.
How many arrangements can be made from the letters of the word " VENUS " such that the order of the vowels remains the same?
Give Introduction to Pythagorean Theorem ? The Pythagorean Theorem says that for any right triangle: a 2 + b 2 = c 2 , where c is the hypotenuse, and a and b are the legs. T
three complain forces of magnitudes 20N 30N and 45N
The Definition- The definition of the Laplace transforms. We will also calculate a couple Laplace transforms by using the definition. Laplace Transforms- As the earlier secti
The radius of the in circle of a triangle is 4cm and the segments into which one side is divided by the point of contact are 6cm and 8cm. Determine the other two sides of the tria
cos(x)y''+sin(x)y=2cos^3(x)sin(x)-1
Proof of Root Test Firstly note that we can suppose without loss of generality that the series will initiate at n = 1 as we've done for all our series test proofs. As well n
l+bx2= 5000+100x2
define algorithm of pert and pert with suitable examples
2
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