000RM.dvi
512 Combinatorial games 17.5 Wythoff’s game .................. Wythoff’s game is a variant of Nim. Given two piles of marbles, a ...
17.5 Wythoff’s game 513 Appendix: Beatty’s Theorem Ifαandβare positive irrational numbers satisfyingα^1 +^1 β=1, then the sequen ...
514 Combinatorial games Exercise 1.What are the winning positions in the battle of numbers withN= 100 andd=7? 2.The golden ratio ...
17.5 Wythoff’s game 515 Project: Another subtraction game Starting with a given positive integer, two players alternately subtra ...
516 Combinatorial games ...
Chapter 18 Repunits 1 k-right-transposable integers 2 k-left-transposable integers 3 Sam Yates’ repunit riddles 4 Recurring deci ...
518 Repunits 18.1 k-right-transposable integers ........... Letkbe a given positive integer. A positive integerXisk-transposable ...
18.2k-left-transposable integers 519 18.2 k-left-transposable integers ........... Letkbe a given positive integer. A positive i ...
520 Repunits 18.3 Sam Yates’ repunit riddles ........... 1.What digits should be substituted for the letters so that the sum of ...
18.3 Sam Yates’ repunit riddles 521 8.Find a pair of repunits whose product is a 100-digit palindrome.^7 9.If a Mersenne numberM ...
522 Repunits 18.4 Recurring decimals ................. vi CONTENTS The decimal expansion of a rational number is eventually peri ...
18.5 The period length of a prime 523 18.5 The period length of a prime ........... The period length of a prime numberpmeans th ...
524 Repunits Appendix: Factorizations of repunitsRnforn≤ 50 nRn 211. 33 × 37. 411 × 101. 541 × 271. 63 × 7 × 11 × 13 × 37. 7239 ...
18.5 The period length of a prime 525 Appendix: Primitive prime divisors of repunits n 211 Primitive prime divisors of. Rn (^33) ...
526 Repunits Appendix: The multiplicative digital root The multiplicative digital root of a number is the single digit number ob ...
18.5 The period length of a prime 527 Exercise 1.What are the decimal expansions of 21 k, 51 k, and 2 h^1 · 5 k? 2.Calculate the ...
528 Repunits Project: Period lengths of primes< 100 Find the period lengths of the primes< 100 by using the factorization ...
18.5 The period length of a prime 529 Project It is known that the number N= 19000458461599776807277716631 is a perfect cube. Fi ...
530 Repunits ...
Chapter 19 More digital trivia 1.Larry, Curly, and Moe had an unusual combination of ages. The sum of any two of the three ages ...
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