Alegbra II Questions?

timer Asked: Feb 27th, 2013

Question description

Ok, I need a better explanation for these two problems:

"Dirichlet was the first to formalize the pigeonhole principle. His idea may be used to solve this problem: A bag of jelly beans contains 335 red, 357 blue, 592 white, 294 orange, and 520 green beans. What is the minimum number of jelly beans that must be selected to guarantee at least one bean of every color. (No peeking.)"

For this problem, I received 1805 as the answer. Can you please prove to me that my answer is correct?

"The Markov equation

x^2 + y^2 + z^2 = 3xyz

has many solutions. If x = 5, there are still an infinite number of solutions, including y = 1 and z = 2 and one other solution with y = 2 and z a prime number. Calculate y^6z to find the year that Markov was born."

Ok, for this one I know his year of birth is 1856 but I don't know how to find that number using the information given above! Please show me the steps I need to take and the math I need to do! 

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