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IOQM Prep Paths
Indian Olympiad Qualifier in Mathematics · 108 reads · 5 chapters
Algebra21 reads
- Alternating sum of squares via telescoping pairs3 min · 1 linked question
- AM-GM equality case in a cyclic system3 min · 1 linked question
- Binary representations and product-of-binomials expansions3 min · 1 linked question
- Complex numbers & systems3 min · 1 linked question
- Consecutive integers, quadratic Diophantine3 min · 1 linked question
- Constrained even-power equations3 min · 1 linked question
- Functional equation solving3 min · 1 linked question
- Inequalities & optimisation3 min · 2 linked questions
- Moving averages monotonicity3 min · 1 linked question
- Percentage equations3 min · 1 linked question
- Piecewise-defined recursive functions3 min · 1 linked question
- Polynomial ratio constraints3 min · 1 linked question
- Polynomial remainder via factorization3 min · 1 linked question
- Polynomials & functional eqns3 min · 1 linked question
- Quadratic-in-x equation with floor(x) as a parameter3 min · 1 linked question
- Sequences & recurrences3 min · 2 linked questions
- Solving a linear functional equation using the substitution x -> 3-x3 min · 1 linked question
- Sum-of-squares decomposition forcing a linear relation3 min · 1 linked question
- Symmetric expressions in cyclic ratios3 min · 1 linked question
- Two-variable linear system for f(x) and f(3-x)3 min · 1 linked question
- Worst-case acute triangle condition over a set of numbers3 min · 1 linked question
Combinatorics26 reads
- 2-coloring a dodecagon avoiding monochromatic equilateral triangles and square3 min · 1 linked question
- Arrangements with a parity constraint3 min · 1 linked question
- Circular coloring with window constraint3 min · 1 linked question
- Combinatorial game with parity strategy3 min · 1 linked question
- Coprime-adjacency constraint counting on a 2x3 grid3 min · 1 linked question
- Counting & enumeration3 min · 2 linked questions
- Counting knight-move pairs on a finite grid3 min · 1 linked question
- Counting permutations with exactly one interior local minimum3 min · 1 linked question
- Counting set-valued functions with required subsets appearing3 min · 1 linked question
- Derangement-type counting3 min · 1 linked question
- Digit constraint counting3 min · 1 linked question
- Extremal & construction3 min · 1 linked question
- Gap-constrained binary strings from a multiplication no-carry condition3 min · 1 linked question
- Geometric combinatorics3 min · 1 linked question
- Graph theory & colouring3 min · 1 linked question
- Guaranteeing a product divisible by 63 min · 1 linked question
- Maximizing visible sums on stacked dice3 min · 1 linked question
- Particle-splitting process with floor division3 min · 1 linked question
- Paths avoiding all-odd-coordinate points3 min · 1 linked question
- Permutations with positional constraint3 min · 1 linked question
- Proper vertex coloring3 min · 1 linked question
- Recursion & compositions3 min · 1 linked question
- Shortest path with two allowed operations3 min · 1 linked question
- Structured counting3 min · 2 linked questions
- Triangle inequality counting3 min · 1 linked question
- Triangle-free 2-colorings of K53 min · 1 linked question
Geometry24 reads
- Cevian ratio combined with a perimeter-like condition3 min · 1 linked question
- Circle geometry3 min · 2 linked questions
- Circumcenter, orthocenter and midpoint relations via vectors3 min · 1 linked question
- Coordinate & metric relations3 min · 1 linked question
- Cube vertices and distance classification3 min · 1 linked question
- Equilateral pedal triangle from an angle-excess condition3 min · 1 linked question
- Finding a third cevian ratio from two given ones using mass points3 min · 1 linked question
- Hexagon formed by tangent lines parallel to the sides of a triangle3 min · 1 linked question
- Inscribed square in a right triangle3 min · 1 linked question
- Integer perimeter and hypotenuse with a fixed altitude3 min · 1 linked question
- Internally tangent circles, perpendicular radius condition3 min · 1 linked question
- Intersection of cevian-like lines in a square3 min · 1 linked question
- Largest square inscribed in a disc of given area3 min · 1 linked question
- Length of a chord through a given interior point parallel to a side3 min · 1 linked question
- Parallelogram diagonal optimization3 min · 1 linked question
- Power of a point and tangent length3 min · 1 linked question
- Quadrilateral diagonal angle splitting3 min · 1 linked question
- Quadrilateral with given sides and angles3 min · 1 linked question
- Quadrilaterals3 min · 2 linked questions
- Rectangle with concyclic points3 min · 1 linked question
- Trapezoids in the coordinate plane3 min · 1 linked question
- Triangle inequality in a quadrilateral3 min · 1 linked question
- Triangle trigonometry3 min · 2 linked questions
- Varignon parallelogram and diagonal perpendicularity3 min · 1 linked question
Inequalities1 read
Number Theory36 reads
- Average-shift condition to determine a set of squares3 min · 1 linked question
- Consecutive integers with divisible digit sums3 min · 1 linked question
- Continuant identity for a 4-term continued fraction3 min · 1 linked question
- Counting pairs with a perfect-square product via squarefree parts3 min · 1 linked question
- Counting smooth numbers3 min · 1 linked question
- Cross-matching sum/product conditions between digit pairs3 min · 1 linked question
- Cylinder surface area = volume3 min · 1 linked question
- Digits & place value3 min · 3 linked questions
- Diophantine equation involving ab, lcm(a,b), gcd(a,b)3 min · 1 linked question
- Distinct remainders of fourth powers3 min · 1 linked question
- Divisibility & modular arithmetic3 min · 3 linked questions
- Divisibility by lcm(1,...,m) over ranges determined by cube roots3 min · 1 linked question
- Divisibility counting3 min · 1 linked question
- Divisibility of repeating-digit numbers3 min · 1 linked question
- Divisibility reduction using gcd properties3 min · 1 linked question
- Divisors of n^2 less than n but not dividing n3 min · 1 linked question
- Exponential Diophantine equation with a perfect square condition3 min · 1 linked question
- Factor pairs and perimeter3 min · 1 linked question
- Factoring a degree-8 polynomial expression via Sophie Germain identity3 min · 1 linked question
- Factoring a two-equation integer system3 min · 1 linked question
- Factorisation & gcd3 min · 1 linked question
- Farey sequence / best rational approximation3 min · 1 linked question
- Last digits of powers3 min · 1 linked question
- LCM equation with gcd substitution3 min · 1 linked question
- Nested radical Diophantine equation3 min · 1 linked question
- Pairing sums into a perfect-square product3 min · 1 linked question
- Perfect squares and cubes3 min · 1 linked question
- Periodicity of 2^n and n^2 modulo 73 min · 1 linked question
- Periodicity of n^n mod p3 min · 1 linked question
- Prime factorization of factorials3 min · 1 linked question
- Repdigit-pattern six-digit numbers equal to a product of consecutive odd numbe3 min · 1 linked question
- Representing powers of 2 as a sum of two positive squares3 min · 1 linked question
- Seven-term continued fraction expansion via the Euclidean algorithm3 min · 1 linked question
- Simultaneous floor-division digit constraints3 min · 1 linked question
- Sum of four distinct primes with an upper bound3 min · 1 linked question
- Sums of two squares3 min · 2 linked questions