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ucsb ccs 130h explore crypto
... Fermat witness in Zn∗ , then the Fermat test on input n gives the correct answer “n is composite” with probability at least 1/2 This theorem says that for many composite numbers (except Carmichael numbers) the Fermat test has a good probability bound The reason why the Fermat test is not a Monte Car ...
... Fermat witness in Zn∗ , then the Fermat test on input n gives the correct answer “n is composite” with probability at least 1/2 This theorem says that for many composite numbers (except Carmichael numbers) the Fermat test has a good probability bound The reason why the Fermat test is not a Monte Car ...
Solutions
... but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had? In the first part of this week’s ...
... but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had? In the first part of this week’s ...
Integer Functions - Books in the Mathematical Sciences
... example, since 18 and 54 belong to the class so do 18 - 54 = -36 and 54 - 18 = 36. We define a module as any class of numbers containing at least two numbers and containing the differences of every pair of numbers in the class. Hence, we say that [0] is a module but [1] and [2] are not. If we take a ...
... example, since 18 and 54 belong to the class so do 18 - 54 = -36 and 54 - 18 = 36. We define a module as any class of numbers containing at least two numbers and containing the differences of every pair of numbers in the class. Hence, we say that [0] is a module but [1] and [2] are not. If we take a ...
THE p–ADIC ORDER OF POWER SUMS, THE ERD
... As an example, take p = 3 and m = 12223 in base 3. In particular, there are three copies of 2 at the end, so we know that V3 (m) = 3. By Theorem 4, for any even n, v3 (Sn (m)) = v3 (S2 (m)) = V3 (m) − 1 = 2. As m = 53, this agrees with the fact that S2 (53) = 53 · 54(2 · 53 + 1)/6 = 51039 = 32 · 53 ...
... As an example, take p = 3 and m = 12223 in base 3. In particular, there are three copies of 2 at the end, so we know that V3 (m) = 3. By Theorem 4, for any even n, v3 (Sn (m)) = v3 (S2 (m)) = V3 (m) − 1 = 2. As m = 53, this agrees with the fact that S2 (53) = 53 · 54(2 · 53 + 1)/6 = 51039 = 32 · 53 ...
