New PDF release: A selection of problems in the theory of numbers

By Waclaw Sierpinski, I. N. Sneddon, M. Stark

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99 105 109 111 115. 111 115 117 121. 119 121 125. 123 127. 131. . 41 + 3 5 7 11 13 17 19 23 29 31 37 41 43 47 3 47 5 49 51 7 51 53 55 11 13 17 19 23 29 31 37 41 43 47 . 55 57 61 63 67 73 75 81 85 87 91 . 57 59 63 65 69 75 77 83 87 89 93 . 59 61 65 67 71 77 79 85 89 91 95 . 63 65 69 71 75 81 83 89 93 95 99 . 67 71 73 77 83 85 91 95 97 101. 75 77 81 87 89 95 99 101 105. 79 83 89 91 97 101 103 107. 87 93 95 101 105 107 111. 99 101 107 111 113 117. 103 109 113 115 119. 115 119 121 125. 123 125 129.

75) Square Residues: 1,2,3,2,5,6,7,2,3,10,11,6,13,14,15,2,17,6,19,10,21,22,23,6,5,26,3,14,29,30, 31,2,33,34,35,6,37,38,39,10,41,42,43,22,15,46,47,6,7,10,51,26,53,6,14,57,58, 59,30,61,62,21,... ) Or, Sr(n) is the number n released of its squares: if n = ( ar a1 ) * ... * ( Pr ), with all p i primes and all ai ≥1, P1 then Sr(n)= p1 * ... * pr . ) are released of their squares. 76) Cubical Residues: 1,2,3,4,5,6,7,4,9,10,11,12,13,14,15,4,17,18,19,20,21,22,23,12,25,26,9,28, 29,30,31,4,33,34,35,36,37,38,39,20,41,42,43,44,45,46,47,12,49,50,51,52,53, 18,55,28,...

And the m-th time digit dm in the front of all k-digits numbers. More general: all digits di can be replaced by numbers as large as we want (therefore of many digits each), and also m can be as large as we want. 117) Square Roots: 0,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5, 6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8, 8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10, 10,10,10,10,10,10,10,10,10,10,10,10,10,10,...

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A selection of problems in the theory of numbers by Waclaw Sierpinski, I. N. Sneddon, M. Stark


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