Challenging Mathematical Problems with Elementary Solutions: Combinatorial analysis and probability theoryHolden-Day, 1964 |
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第 1 到 3 筆結果,共 18 筆
第 29 頁
... prime to 6 ? That at least one of two integers selected at random is relatively prime to 6 ? 87a . What is the probability that the square of an integer selected at random will end with the digit 1 ? That the cube of an integer selected ...
... prime to 6 ? That at least one of two integers selected at random is relatively prime to 6 ? 87a . What is the probability that the square of an integer selected at random will end with the digit 1 ? That the cube of an integer selected ...
第 59 頁
... prime . Another example of such a function is Euler's function ( N ) , the number of positive integers ≤ N and relatively prime to N ( see the remark to problem 14 ) . = Thus ( N ) and o ( N ) are multiplicative functions . Note ...
... prime . Another example of such a function is Euler's function ( N ) , the number of positive integers ≤ N and relatively prime to N ( see the remark to problem 14 ) . = Thus ( N ) and o ( N ) are multiplicative functions . Note ...
第 195 頁
... prime to 6 , and of the next R integers , at most two can be relatively prime to 6 ( since R is at most 5 ) . Thus a total of 20 + r integers from 1 to N are relatively prime to 6 , where r is 0 , 1 , or 2. Consequently , the ...
... prime to 6 , and of the next R integers , at most two can be relatively prime to 6 ( since R is at most 5 ) . Thus a total of 20 + r integers from 1 to N are relatively prime to 6 , where r is 0 , 1 , or 2. Consequently , the ...
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A₁ A₂ An+m arrangements b₁ B₂ binomial coefficients binomial theorem bishops black squares C₁ chessboard chord circle coefficient color column compute the number Consequently consider corresponding customers denote determine the number diagonals digits dihedral angle divided divisible draw equally likely possible equation equidistant equivalence classes exactly example experiment favorable outcomes follows formula G₁ given Hence inclusion and exclusion intersection k-gons knights length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks S₁ segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices