Number Theory

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

Problems in this category

The problem presents a subtraction problem in base 7, where one digit in the result is missing. We ...

Number BaseBase 7SubtractionArithmetic
2025/4/29

The problem consists of two parts. The first part concerns a six-digit number $M$ of the form $xyzzy...

Divisibility RulesModular ArithmeticBase ConversionCryptographyLeast Common Multiple
2025/4/28

Safiya, Sarah, and Ramli obtained marks of $1001100_2$, $121_x$, and $1103_4$ respectively in a math...

Number Base ConversionBinaryQuaternaryOctalBase Conversion Arithmetic
2025/4/26

The problem provides the heights of Anas, Iman, and Muaz in different bases. Anas's height is $10100...

Number BasesBase Conversion
2025/4/26

The problem describes a rectangle ABCD with a length of $30_8$ and a width of $100_6$. (a) The first...

Number Base ConversionBase ConversionArithmeticPerimeter Calculation
2025/4/26

The problem asks us to arrange the following numbers in ascending order: $57_8$, $2E_{16}$, $65$, $1...

Number Base ConversionsOrdering Numbers
2025/4/20

The problem asks to simplify $(11_{two})^2$. The answer should be expressed in base 2.

Number BasesBinary NumbersExponentsBase Conversion
2025/4/11

We are given the equation $101_{two} + 12_y = 23_{five}$, and we need to find the value of $y$. The ...

Number BasesBase ConversionEquation Solving
2025/4/10

Problem 4 asks us to find the least value of $x$ that satisfies the equation $4x \equiv 7 \pmod{9}$....

Modular ArithmeticCongruencesLogarithmsModular Inverse
2025/4/10

A school bus has to make three complete trips. The times, in minutes, for the three trips are $254_6...

Number BasesBase Conversion
2025/4/10