Number Theory

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

Problems in this category

The problem asks us to identify which of the given numbers is an irrational number. The options are ...

Irrational NumbersReal NumbersRational NumbersSquare Roots
2025/6/8

The problem is to convert the binary number $10101_2$ to its equivalent decimal (base 10) representa...

Number SystemsBinary NumbersDecimal ConversionBase Conversion
2025/6/7

We are asked to convert the number $23$ from base ten to base two.

Number BasesBase ConversionBinary Representation
2025/6/7

The problem states that if $n$ is an odd integer, then $n^2 + 3n + 5$ is odd. We need to prove wheth...

Number TheoryParityOdd and Even IntegersProof
2025/6/7

The problem states that if $n$ is an odd integer, then $n^3$ is odd. We need to prove this statement...

Integer PropertiesOdd and Even NumbersProof by direct method
2025/6/7

The problem asks us to prove three statements using the direct proof method: i) If $n$ is an even in...

ProofsEven and Odd NumbersInteger PropertiesDirect Proof
2025/6/7

The problem asks us to prove that if $n$ is an even integer, then $n^2$ is even, using a direct proo...

Even NumbersProof by Direct ProofInteger PropertiesDivisibility
2025/6/7

The problem asks to find the 8-bit binary representation of the number 26, where one bit is used for...

Binary RepresentationNumber ConversionBase Conversion
2025/6/7

The problem asks to convert the two's complement binary number $11100011$ to its decimal representat...

Binary NumbersTwo's ComplementNumber Base Conversion
2025/6/7

The problem asks to find the denary (decimal) representation of the 8-bit signed binary number $1000...

Binary NumbersTwo's ComplementNumber RepresentationComputer ScienceBitwise Operations
2025/6/7