Number Theory
Problems related to integers, prime numbers, congruences, etc.
Problems in this category
The problem requires us to fill in the blank with the missing Roman numeral to complete the given se...
Roman NumeralsNumber SequencesNumber Conversion
2025/7/15
We are given three numbers: 1985, 6814, and 3741. We need to find the largest number $x$ such that w...
Greatest Common DivisorEuclidean AlgorithmRemainder Theorem
2025/7/8
The problem asks to find a Pythagorean triplet whose smallest member is 8. The general form of the P...
Pythagorean TriplesNumber TheoryInteger Solutions
2025/7/2
Prove by induction that for every positive integer $n$, $3^{2n} - 1$ is divisible by 8.
DivisibilityInductionInteger Properties
2025/7/1
The problem is to find the next number in the sequence: $1, 5, 14, 30, 55, ...$
SequencesNumber PatternsDifference Sequences
2025/6/26
The image shows a sequence of numbers: $-1, 2, 7, 114, 2233, \dots$ The problem is to find a pattern...
SequencesPattern RecognitionRecurrence RelationsNumber Sequences
2025/6/25
We need to find all natural numbers $n$ such that $\sqrt{\frac{72}{n}}$ is a natural number.
DivisibilitySquare RootsInteger PropertiesPerfect Squares
2025/6/24
The problem asks us to find the smallest natural number that, when multiplied by 135, results in a p...
Prime FactorizationPerfect SquaresInteger Properties
2025/6/24
The problem asks: How many different pairs of positive integers have a greatest common factor (GCF) ...
Greatest Common Factor (GCF)Least Common Multiple (LCM)Prime FactorizationRelatively PrimeNumber of Pairs
2025/6/14
The problem asks which of the given set membership statements are correct. A. $\frac{7}{3} \notin N$...
Set TheoryNumber SetsNatural NumbersIntegersRational NumbersReal NumbersSet Membership
2025/6/14