+0  
 
0
123
1
avatar+50 

How many of the 1000 smallest positive integers are congruent to 1 modulo 9?

Atroshus  Aug 17, 2017
Sort: 

1+0 Answers

 #1
avatar
0

You should have ALL the multiples of 9 + 1, up to 1,000. So, 999 / 9 = 111. You would use: 9n + 1, from n=1 to 111. And the sequence of these numbers would be:

 

{10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 199, 208, 217, 226, 235, 244, 253, 262, 271, 280, 289, 298, 307, 316, 325, 334, 343, 352, 361, 370, 379, 388, 397, 406, 415, 424, 433, 442, 451, 460, 469, 478, 487, 496, 505, 514, 523, 532, 541, 550, 559, 568, 577, 586, 595, 604, 613, 622, 631, 640, 649, 658, 667, 676, 685, 694, 703, 712, 721, 730, 739, 748, 757, 766, 775, 784, 793, 802, 811, 820, 829, 838, 847, 856, 865, 874, 883, 892, 901, 910, 919, 928, 937, 946, 955, 964, 973, 982, 991, 1000}. So that: (9n + 1) mod 9 = 1.

Guest Aug 17, 2017

4 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details