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Let a, b, c 2 Z+.
(a) Prove that if a|b, then ac|bc for all c.
(b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
(c) Prove that gcd(a, a + b) = gcd(a, b).
Explain the rules of Divisibility ? Divisible by 2: If the last digit is a 0, 2, 4, 6, or 8, the number is evenly divisible by 2. Divisible by 2 Not
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Even and Odd Functions : This is the final topic that we have to discuss in this chapter. Firstly, an even function is any function which satisfies,
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Now we have to discuss the basic operations for complex numbers. We'll begin with addition & subtraction. The simplest way to think of adding and/or subtracting complex numbers is
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