- #1
thecleric
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Homework Statement
Suppose that we play the following game. You are given a pile of N matches. You break the pile into two smaller piles of m and n matches. Then you form the product 2mn and remember it. Next, you take one of the piles and break it into two smaller piles (if possible), say of m’ and n’ matches. You form the product 2m’n’ and add it to the 2mn that you had before, so now you have 2mn+2m’n’. You proceed again by breaking one of the piles into two and adding the resulting product. The process is finished when you finally have N piles of one match in each. By convention, if N = 1 then you don't do anything and the result is 0. Try to take a pile of five matches and play this game several times, each time breaking to piles in a different way. What do you see?
If you start with a pile of matches, no matter how you break it, the sum of the computed products will always be .
Homework Equations
The Attempt at a Solution
Can someone explain this to me?
Homework Statement
Prove that An<[tex]\left([/tex]7/4)n
Homework Equations
n greater than or equal to 3
The Attempt at a Solution
Homework Statement
Prove statement below by contrapositive and contradiction:
If a prime number divides the square of an integer, then that prime number divides that integer.
Homework Equations
n is prime for all positive integers r and s if n=rs where r=1 or s=1
The Attempt at a Solution
Basically let m be a prime number, if m divides n2 then m divides n
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