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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.
proof of chebychevs lemma
The Cartesian product (also called as the cross product) of two sets A and B, shown by AΧB (in the similar order) is the set of all ordered pairs (x, y) such that x€A and y€B. What
Q. What is a percentage? Ans. Percent means "per hundred", or "out of 100". A percentage can be written as a ratio, or fraction, where the denominator (bottom) is 100.
Fermat Catalan Conjecture
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joey asked 30 randomly selected students if they drank milk, juice, or bottled water with their lunch. He found that 9 drank milk, 16 drank juice, and 5 drank bottled water. If the
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Continuity : In the last few sections we've been using the term "nice enough" to describe those functions which we could evaluate limits by just evaluating the function at the po
Critical point of exponential functions and trig functions, Let's see some examples that don't just involve powers of x. Example: find out all the critical points for the
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