Challenging Mathematical Problems with Elementary Solutions, 第 1 卷Holden-Day, 1964 - 440 頁 |
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第 1 到 3 筆結果,共 18 筆
第 29 頁
... prime to 6 ? 87a . What is the probability that the square of an integer selected at random will end with the digit ... prime . Prove that exists . lim SN = S N → ∞ 93. Show that the infinite series 1 + 1 1 VII . Experiments with ...
... prime to 6 ? 87a . What is the probability that the square of an integer selected at random will end with the digit ... prime . Prove that exists . lim SN = S N → ∞ 93. Show that the infinite series 1 + 1 1 VII . Experiments with ...
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 7 ( N ) and σ ( 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 7 ( N ) and σ ( 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 2Q + 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 2Q + 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 given Hence inclusion and exclusion intersection k-gons knights L₁ length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane points A1 polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices