|By Loop123 (Loop123) on Friday, July 09, 2004 - 06:02 pm: Edit|
1.How many of the integers between 1 and 1,000 , inclusive, can be expressed as the difference of the squares of two nonnegative integers?
2.For how many values of k is 12^12 the least common multiple of the positive integers 6^6, 8^8, and k?
3.Find the smallest prime that is the fifth term of an increasing arithmetic sequence, all four preceding terms being also prime.
|By Loop123 (Loop123) on Friday, July 09, 2004 - 06:51 pm: Edit|
Anyone up for the challenge?
|By Albertfermat (Albertfermat) on Friday, July 09, 2004 - 07:04 pm: Edit|
they r pretty easy, especially if u have done all of them
|By Feuler (Feuler) on Friday, July 09, 2004 - 07:10 pm: Edit|
In case other people want to try these but get stuck, here are a couple hints. These particular problems aren't too difficult, as AIME problems go.
1- Factor a^2-b^2.
2- Use prime factorization.
3- Think about what values the comman difference can be, keeping in mind that no two members of the sequence can share any prime factors.
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