Revisiting a Number-Theoretic Puzzle: The Census
... What are the ages of the children? With seemingly insufficient information, such number-theoretic puzzles belong to what is now known as the census-taker problem. To someone encountering the problem for the first time, the information transpired during the conversation is not sufficient to determine ...
... What are the ages of the children? With seemingly insufficient information, such number-theoretic puzzles belong to what is now known as the census-taker problem. To someone encountering the problem for the first time, the information transpired during the conversation is not sufficient to determine ...
Grade 6 Math Curriculum
... Example 1: Given a story context for (2/3) ÷ (3/4), explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces ca ...
... Example 1: Given a story context for (2/3) ÷ (3/4), explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces ca ...
Pseudoprimes and Carmichael Numbers, by Emily Riemer
... Finally, if n is a Carmichael number, it must also satisfy an−1 ≡ 1 (mod n). Because we have defined (6k + 1), (12k + 1), and (18k + 1) to be prime, we know by Fermat’s Little Theorem that api −1 ≡ 1 (mod pi ). We want to show that an−1 ≡ 1 (mod pi ), and then use the Chinese Remainder Theorem to sh ...
... Finally, if n is a Carmichael number, it must also satisfy an−1 ≡ 1 (mod n). Because we have defined (6k + 1), (12k + 1), and (18k + 1) to be prime, we know by Fermat’s Little Theorem that api −1 ≡ 1 (mod pi ). We want to show that an−1 ≡ 1 (mod pi ), and then use the Chinese Remainder Theorem to sh ...
manembu - William Stein
... Introduction. Continued fractions provide a unique method of expressing numbers or functions, different from the more commonly used forms introduced throughout grade school math classes and beyond. At first glance, continued fractions may seem like they are just a more complex way to say something s ...
... Introduction. Continued fractions provide a unique method of expressing numbers or functions, different from the more commonly used forms introduced throughout grade school math classes and beyond. At first glance, continued fractions may seem like they are just a more complex way to say something s ...
Full text
... However, suppose the nth term is [ (3 + l//29~)n], or perhaps [(4 - 5//57)n] , where [x] means the greatest integer <. x. In these sequences, 15 is followed by 19 rather than 18. Such almost arithmetic sequences have many interesting properties which have been discovered only in recent years. Of spe ...
... However, suppose the nth term is [ (3 + l//29~)n], or perhaps [(4 - 5//57)n] , where [x] means the greatest integer <. x. In these sequences, 15 is followed by 19 rather than 18. Such almost arithmetic sequences have many interesting properties which have been discovered only in recent years. Of spe ...
Holt McDougal Algebra 1 6-2
... population P of a bacteria colony is given by , where t is the number of days since start of the experiment. Find the population of the colony on the 8th day. Simplify. All variables represent nonnegative ...
... population P of a bacteria colony is given by , where t is the number of days since start of the experiment. Find the population of the colony on the 8th day. Simplify. All variables represent nonnegative ...
