Number Theory

Problems related to integers, prime numbers, congruences, etc.

Problems in this category

The problem states that Indah Hotel offers free breakfast to guests aged 6 years and below. Guests o...

Number Base ConversionBase ConversionArithmetic
2025/4/10

A pipe is cut into three equal parts. The lengths are given as $0$, $30_4$, $x_6$, and $121_5$. We n...

Number BasesBase ConversionArithmetic
2025/4/10

The problem asks to identify which of the following number conversions is true: A. $11001_2 = 39_{10...

Number Base ConversionsBase 2Base 8Base 5Base 10
2025/4/10

The problem asks for the base-10 value of the underlined digit '6' in the base-8 number $2673_8$.

Number BasesBase ConversionPositional Notation
2025/4/10

Question 9: Find the binary, hexadecimal, or octal number that is equivalent to the decimal value 16...

Number Base ConversionsBinaryHexadecimalOctalDecimal
2025/4/8

The problem asks us to fill in a 2x2 table with numbers less than 100. The rows are "a square number...

Number PropertiesSquare NumbersEven and Odd Numbers
2025/4/4

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