Math Problem Statement
After training for her entire life, Erica is approaching the pinnacle of her Tennis career. She is about to compete in the Women’s Singles Tennis finals at the Olympics and has a shot at gold. But disaster... while sitting in the locker room, she has started experiencing pre-competition nerves because she cannot f igure out the following problems. (a) If x and y are both divisible by k, prove that gcd(x,y) = k ·gcd(x k, y k), where k > 1.
Solution
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Math Problem Analysis
Mathematical Concepts
Number Theory
Greatest Common Divisor (GCD)
Divisibility
Formulas
gcd(x, y) = k · gcd(x/k, y/k)
Theorems
Properties of GCD
Divisibility Rules
Suitable Grade Level
University Level (Number Theory)