- **Puzzles**
(*https://www.mersenneforum.org/forumdisplay.php?f=18*)

- - **Easy number theory.**
(*https://www.mersenneforum.org/showthread.php?t=5940*)

Easy number theory.:question:
A 3 digit number in the scale of 7 has its digits reversed when expressed in the scale of 9. Find the number in all three scales, 7 ,9 and 10. Mally :coffee: |

[spoiler]49k+7m+n = 81n+9m+k
48k-2m-80n = 0 24k-m-40n = 0 1<=k<=6 0<=m<=6 1<=n<=6 m must be multiple of gcd(24,40) = 8, so m=0 m = 0 -> 24k-40m = 0 -> k=5, n=3 So the number in base 7 is 503 (248 decimal), which is equal to 305 in base 9.[/spoiler] |

Easy number theory.:redface:
Fine deduction Alpertron! I thought the digit 8 coming in to the calculations would stump any one in forming the equations. I must bear you in mind when I give my next problem and make it more challenging. Mally :coffee: |

All times are UTC. The time now is 06:56. |

Powered by vBulletin® Version 3.8.11

Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.