2020-02-14, 15:19 | #1 |
Mar 2018
17·31 Posts |
cubes congruent to 2^n (mod 215)
1^3 is congruent to 2^n (mod 215) n=0
6^3 is congruent to 2^n (mod 215) n=0 7^3 is congruent to 2^n (mod 215) n=7 any other cubes congruent to 2^n (mod 215)? Last fiddled with by enzocreti on 2020-02-14 at 15:23 |
2020-02-14, 16:56 | #2 |
"Dylan"
Mar 2017
553_{10} Posts |
Firstly, since n+215k is n mod 215 for any n and k in the integers, we know that (1+215k)^3 must be 1 mod 215 = 2^0 mod 215, and similarly for the others cases stated ((6+215k)^3 = 2^0 mod 215, and (7+215k)^3 = 2^7 mod 215).
So it suffices to check on the integers in the set [0, 214], then use the equivalence classes to quickly generate the rest. |
Thread Tools | |
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
sum of two positive cubes congruent to 1 mod Mersenne prime | enzocreti | enzocreti | 2 | 2020-02-14 12:36 |
Fibonacci number as sum of cubes | jux | Miscellaneous Math | 15 | 2015-08-30 06:21 |
Squares and Cubes: | mfgoode | Puzzles | 24 | 2007-08-06 16:20 |
Prime cubes! | fivemack | Puzzles | 4 | 2007-07-04 00:18 |
Counting Cubes | Numbers | Puzzles | 6 | 2005-09-03 00:26 |