This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND
OR
NO

Found problems: 3

2024 Czech-Polish-Slovak Junior Match, 5
Is there a positive integer $n$ such that when we write the decimal digits of $2^n$ in opposite order, we get another integer power of $2$?
digit palindrome powers of 2 number theory digits

2020 Brazil National Olympiad, 3
Consider an inifinte sequence $x_1, x_2,\dots$ of positive integers such that, for every integer $n\geq 1$: [list] [*]If $x_n$ is even, $x_{n+1}=\dfrac{x_n}{2}$; [*]If $x_n$ is odd, $x_{n+1}=\dfrac{x_n-1}{2}+2^{k-1}$, where $2^{k-1}\leq x_n<2^k$.[/list] Determine the smaller possible value of $x_1$ for which $2020$ is in the sequence.
powers of 2 number theory sequences

ICMC 4, 5
Find all composite positive integers \(m\) such that, whenever the product of two positive integers \(a\) and \(b\) is \(m\), their sum is a power of $2$. [i]Proposed by Harun Khan[/i]
elementary-number-theory powers of 2 number theory modular arithmetic