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extra credit 1

extra credit 1 - so that 2 n n is not divisible by 3 or...

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1. Postage stamps Suppose you have an unlimited number of A cent postage stamps and B cent postage stamps, where A and B have no common divisor greater than 1. What is the largest total that you can not make using these stamps? Recall that in class we did the case with A = 3 and B = 5, and in this case, the largest value you could not make was 7. 2. The middle binomial coefficient ( 2 n n ) . (i) Show that ( 2 n n ) is always even . (ii) Show that there are infinitely many values of n
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Unformatted text preview: so that ( 2 n n ) is not divisible by 3 or 5. (iii) ($1000) Show that there infinitely many values of n so that ( 2 n n ) is not divisible by 3 , 5 or 7. (iv) ($1000) Show that there are only finitely many values of n so that ( 2 n n ) is not divisible by 3 , 5 , 7 or 11. Note : I don’t really expect anyone to solve (ii), (iii) or (iv) but computing some data might give a clue as to what is going on. 1...
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  • Fall '07
  • Graham
  • Fraction, Negative and non-negative numbers, Prime number, Greatest common divisor, Postage stamp, cent postage stamps

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