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Space ElevatorTime Limit: 1000MSMemory Limit: 65536KTotal Submissions: 6236Accepted: 2883DescriptionThe cows are going to space! They plan to achieve orbit by building a sort of space elevator: a giant tower of blocks. They have K (1 <= K <= 400) different types of blocks with which to build t 阅读全文
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InvestmentTime Limit: 1000MSMemory Limit: 30000KTotal Submissions: 5419Accepted: 1874DescriptionJohn never knew he had a grand-uncle, until he received the notary's letter. He learned that his late grand-uncle had gathered a lot of money, somewhere in South-America, and that John was the only in 阅读全文
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Charm BraceletTime Limit: 1000MSMemory Limit: 65536KTotal Submissions: 13771Accepted: 6272DescriptionBessie has gone to the mall's jewelry store and spies a charm bracelet. Of course, she'd like to fill it with the best charms possible from the N (1 ≤ N ≤ 3,402) available charms. Each charm 阅读全文
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Primitive Roots Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u Submit Status Practice POJ 1284DescriptionWe say that integer x, 0 < x < p, is a primitive root modulo odd prime p if and only if the set { (xi mod p) | 1 <= i <= p-1 } is equal to { 1, ..., p-1 }. F 阅读全文
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Prime Distance Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u Submit Status Practice POJ 2689DescriptionThe branch of mathematics called number theory is about properties of numbers. One of the areas that has captured the interest of number theoreticians for thousands of ye 阅读全文
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J - Goldbach's Conjecture Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u Submit Status Practice POJ 2909DescriptionFor any even number n greater than or equal to 4, there exists at least one pair of prime numbers p1 and p2 such thatn = p1 + p2This conjecture has not bee 阅读全文
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I - Goldbach's Conjecture Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u Submit Status Practice POJ 2262DescriptionIn 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture: Every even number g 阅读全文
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H - Perfect Pth Powers Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u Submit Status Practice POJ 1730DescriptionWe say that x is a perfect square if, for some integer b, x = b2. Similarly, x is a perfect cube if, for some integer b, x = b3. More generally, x is a perfect pt 阅读全文
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Pseudoprime numbers Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u Submit Status Practice POJ 3641DescriptionFermat's theorem states that for any prime number p and for any integer a > 1, ap = a (mod p). That is, if we raise a to the pth power and divide by p, the re 阅读全文
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Prime GapTime Limit: 5000MSMemory Limit: 65536KTotal Submissions: 6841Accepted: 3946DescriptionThe sequence of n − 1 consecutive composite numbers (positive integers that are not prime and not equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For e 阅读全文
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Sum of Consecutive Prime NumbersTime Limit: 1000MSMemory Limit: 65536KTotal Submissions: 13861Accepted: 7748DescriptionSome positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representations does a given positive integer have? For example, the integ 阅读全文
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Prime LandTime Limit: 1000MSMemory Limit: 10000KTotal Submissions: 2074Accepted: 957DescriptionEverybody in the Prime Land is using a prime base number system. In this system, each positive integer x is represented as follows: Let {pi}i=0,1,2,... denote the increasing sequence of all prime numbers. 阅读全文