Afaceinthematrix

Did anyone participate in the 2009 Putnam Competition yesterday? I thought that the test was slightly easier than last years exam. One problem on the exam that I thought was particularly interesting was problem 1B:

Prove that every positive rational number can be written as a quotient of factorials of primes.

That problem took me about half an hour or so to figure out. I ended up coming up with an elegant proof by contradiction showing that if it cannot be written as that way, then it will end up contradicting both the definition of a rational number and the Fundamental Theorem of Arithmetic.

Did anyone else participate in the competition yesterday? I can't wait to see the results... Too bad we have to wait until the end of March to find out how we did...

Prove that every positive rational number can be written as a quotient of factorials of primes.

That problem took me about half an hour or so to figure out. I ended up coming up with an elegant proof by contradiction showing that if it cannot be written as that way, then it will end up contradicting both the definition of a rational number and the Fundamental Theorem of Arithmetic.

Did anyone else participate in the competition yesterday? I can't wait to see the results... Too bad we have to wait until the end of March to find out how we did...