My Problem Collection
A comprehensive collection of mathematical problems spanning multiple areas of mathematics.
28 mathematical problems spanning algebra, number theory, analysis, and combinatorics.
Note:Problems invented by me are labelled with an asterisk (*), while golden cards indicate problems from my Brilliant.org collection (2013-2015). Many more problems and solutions from my preparation years can be found on Oliforum, the Italian Math Olympics community forum.
Algebra
Equations, polynomials, and algebraic structures
A Triangle Polynomial
A geometric problem involving polynomial relationships within triangular configurations.
Sum of Squares Formula
Derive a closed formula for the sum of the first n perfect squares.
Polynomial Functional Equation
Find all polynomials satisfying a specific functional equation.
System with Powers
Solve a system of equations involving powers of three variables.
Trigonometric Inequality
Prove an inequality involving square roots using a clever substitution.
Nested Radical*
Evaluate a complex nested radical expression.
Golden Ratio Series
Evaluate an infinite series involving the golden ratio.
Polynomial with Roots of Unity
Find the sum of coefficients with indices divisible by 3.
Fibonacci Polynomial Extension
Extend the Fibonacci sequence using polynomial interpolation.
Nested Square Root
Evaluate an infinite nested square root.
Number Theory
Properties of integers, divisibility, and modular arithmetic
3 Factors = 2 Factors?
A number theory problem exploring the relationship between different factorization approaches.
Consecutive Perfect Squares
An interesting problem exploring the properties and relationships of consecutive perfect squares.
Sum of Fifth Powers
A challenging problem involving the sum 1⁵+2⁵+...+n⁵ and its mathematical properties.
Find p
A problem that challenges solvers to find the value of p through logical deduction and mathematical reasoning.
Missing Digit in 2^29
Find which digit from 0-9 is missing in the decimal representation of 2^29.
Pythagorean n-tuples
Prove the existence of Pythagorean triples for any power.
Four-Digit Automorphic Number
Find a number whose square ends with itself.
First Digit of Powers
Determine the common first digit of powers of 2 and 5.
Diophantine Equation with Powers
Find all integer solutions to an equation involving powers of 2 and 5.
Factorial vs Power Comparison
Compare the size of a factorial with a power.
Arithmetic Progression of Primes
Find all 7-term arithmetic progressions consisting entirely of primes.
Pythagorean Reciprocals
Prove that Pythagorean triples cannot satisfy a related reciprocal equation.
Infinite Product
Evaluate an infinite product involving quadratics.
Two-Digit Number Puzzle*
Find a number satisfying a specific digital property.
Combinatorics & Probability
Counting, arrangements, and probability
Guess the Digits
A logic problem that challenges players to deduce the correct sequence of digits through systematic reasoning.
Consecutive Composite Numbers
Prove the existence of arbitrarily long sequences of composite numbers.
Circular Game Board Probability*
Calculate steady-state probabilities in a Markov chain game.
Geometry
Spatial reasoning and geometric constructions
Explore More
Discover how my diverse interests have shaped my professional path.