Prove that for any $n > 1$, the polynomial
$P(x) = 2008x^n + 7x + 56$
cannot be factored into two non-trivial integer polynomials.
(A polynomial is non-trivial if its highest degree is greater than one)
Showing posts with label 2008. Show all posts
Showing posts with label 2008. Show all posts
Monday, August 17, 2009
KBB2 Problem 6
An integer is called homogenous if its decimal representation consists of 1 number. For example, 11 and 222 are homogenous. Prove that there are infinitely many homogeneous numbers that are divisible by 2008.
Sunday, August 16, 2009
KBB2 Problem 2
The country of Sikinia uses gold, silver, and bronze coins as its currency. One gold coin is worth 334 silver coins, and one silver coin is worth 208 bronze coins. One day, Ali went to the store and bought an item priced at 3 gold coins. How many ways can Ali pay the item in, assuming that he has unlimited supply of gold, silver, and bronze coins?
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