Number Theory
Problems related to integers, prime numbers, congruences, etc.
Problems in this category
We have four digit cards: 7, 5, 2, and 1. We need to choose two cards each time to make two-digit nu...
DivisibilityFactorsMultiplesSquare Numbers
2025/4/4
We are given that a positive integer $N$ is represented as $abc$ in base 5 and $cba$ in base 9. We w...
Number BasesBase ConversionDiophantine Equations
2025/3/31
The problem asks to find the hexadecimal equivalent of $X+Y$, where $X = 10010_2$ and $Y = 1111_2$ a...
Number SystemsBinaryHexadecimalBase ConversionArithmetic Operations
2025/3/31
The image presents multiple-choice questions. We will solve questions 34, 35, 36, and 37. Question 3...
Modular ArithmeticModulo Operation
2025/3/31
We are asked to find which of the given numbers cannot be the base of the number $12012$.
Number BasesBase Conversion
2025/3/31
The problem asks us to classify given numbers into different sets of numbers: - N: Natural numbers -...
Number SetsReal NumbersRational NumbersIrrational NumbersIntegersNatural Numbers
2025/3/30
We are given the number 243, which is not a perfect square. We need to find the smallest natural num...
Perfect SquaresPrime FactorizationInteger Properties
2025/3/30
The problem asks us to find the smallest natural number that we need to divide 675 by to obtain a pe...
Prime FactorizationPerfect SquaresDivisibility
2025/3/30
Determine whether the number $\frac{\pi}{5}$ is rational or irrational.
Rational NumbersIrrational NumbersReal NumbersPi
2025/3/21
The problem asks whether the number $7.11$ is rational or irrational.
Rational NumbersIrrational NumbersNumber Representation
2025/3/21