olymmath

BALTIC-WAY 2023 Problem 17

  • Answer

Let S(m)S(m) be the sum of the digits of the positive integer mm. Find all pairs (a,b)(a, b) of positive integers such that S(ab+1)=abS\left(a^{b+1}\right)=a^{b}.

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

(a, b) \in\left{(1, b) \mid b \in \mathbb{Z}^{+}\right} \cup{(3,2),(9,1)}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Locator baltic-way/2023/p17 · Tag 1TC2DQM0JB · Edit this page on GitHub · Keys: j next, k previous