I'm new to proofs, and am trying to solve this problem from William J. Gilbert's "An Introduction To Mathematical Thinking: Algebra and Number Systems". Specifically, this is from Problem Set 2 Question 74. It asks:
How to prove or disprove that gcd?
What I've tried is to use the proposition that \gcd(a, b) = ax + by to rewrite the whole equality, but I can't manage to equate the two statements.
Any help would be appreciated.
Answer
Notice if a = b = c = 3, then
\gcd(ab,c) = \gcd(9,3) = 3
while
gcd(a,b) \times gcd(b,c) = gcd(3,3) \times gcd(3,3) = 3 \times 3 = 9
\therefore gcd(ab,c) \neq gcd(a,b)\times gcd(b,c)
No comments:
Post a Comment