Number Theory
Problems related to integers, prime numbers, congruences, etc.
Problems in this category
The problem asks to find the greatest common factor (G.C.F.) of the numbers 30, 45, and 60, given th...
Greatest Common FactorGCDPrime FactorizationInteger Properties
2025/5/26
The problem asks us to find which of the given numbers (11,116, 16,462, 21,240, 28,814) is divisible...
Divisibility RulesInteger PropertiesDivisibility by 2Divisibility by 3Divisibility by 6
2025/5/26
We are given that $x$, $y$, and $z$ are natural numbers such that $1 < x < y < z$, and we need to fi...
Diophantine EquationsInequalitiesInteger Solutions
2025/5/25
The problem asks us to find all triples of natural numbers $(x, y, z)$ such that $1 < x < y < z$ and...
Diophantine EquationsInequalitiesNumber Theory
2025/5/25
We are given that $x, y, z$ are natural numbers such that $1 < x < y < z$ and $(1 + \frac{1}{x})(1 +...
Diophantine EquationsInequalitiesInteger SolutionsNumber Theory
2025/5/25
We are given the HCF (highest common factor) and LCM (least common multiple) of two numbers, and one...
HCFLCMNumber Properties
2025/5/20
The problem consists of filling in the blanks in sentences related to number theory.
Number PropertiesEven NumbersOdd NumbersInteger Properties
2025/5/18
We are asked to find $\varphi(n)$ for $n \le 310$ and we are given $n = 4$. It is presumed we have t...
Euler's Totient FunctionNumber TheoryPrime Factorization
2025/5/7
The problem asks us to list the factors of the number 30. A factor of a number is an integer that di...
FactorsDivisibilityInteger Properties
2025/5/7
The problem asks to find the factors of 30.
FactorsDivisibilityInteger Properties
2025/5/7