MathDB

1.3

Part of 2010 Saudi Arabia Pre-TST

Problems(1)

b divides a^n - 1, multiple of 7^{2010} of the form 99... 9

Source: 2010 Saudi Arabia Pre-TST 1.3

12/28/2021
1) Let aa and bb be relatively prime positive integers. Prove that there is a positive integer nn such that 1≤n≤b1 \le n \le b and bb divides an−1a^n - 1.
2) Prove that there is a multiple of 720107^{2010} of the form 99...999... 9 (nn nines), for some positive integer nn not exceeding 720107^{2010}.
number theorydividesDigitsdivisible