https://mathgoldmedalist.com/1.0 https://mathgoldmedalist.com/toolkit https://mathgoldmedalist.com/toolkit/sum-first-n-integers https://mathgoldmedalist.com/toolkit/sum-of-squares https://mathgoldmedalist.com/toolkit/sum-of-cubes https://mathgoldmedalist.com/toolkit/geometric-series https://mathgoldmedalist.com/toolkit/telescoping-series https://mathgoldmedalist.com/toolkit/square-of-a-sum https://mathgoldmedalist.com/toolkit/square-of-a-difference https://mathgoldmedalist.com/toolkit/cube-of-a-sum https://mathgoldmedalist.com/toolkit/cube-of-a-difference https://mathgoldmedalist.com/toolkit/difference-of-squares https://mathgoldmedalist.com/toolkit/difference-of-cubes https://mathgoldmedalist.com/toolkit/sum-of-cubes-factored https://mathgoldmedalist.com/toolkit/general-difference-of-powers https://mathgoldmedalist.com/toolkit/sum-of-odd-power https://mathgoldmedalist.com/toolkit/difference-of-even-power https://mathgoldmedalist.com/toolkit/hockey-stick-identity https://mathgoldmedalist.com/toolkit/vandermondes-identity https://mathgoldmedalist.com/toolkit/symmetric-cubic-sum https://mathgoldmedalist.com/toolkit/factoring-quadratic-by-grouping https://mathgoldmedalist.com/toolkit/binomial-theorem https://mathgoldmedalist.com/toolkit/quadratic-formula https://mathgoldmedalist.com/toolkit/approaches-to-similar-equations https://mathgoldmedalist.com/toolkit/sfft https://mathgoldmedalist.com/toolkit/square-of-a-sum-n-terms https://mathgoldmedalist.com/toolkit/arithmetic-sequence-and-series https://mathgoldmedalist.com/toolkit/expansion-of-three-binomials https://mathgoldmedalist.com/toolkit/expansion-of-two-binomials https://mathgoldmedalist.com/toolkit/max-qm-am-gm-hm-min-inequality https://mathgoldmedalist.com/toolkit/integer-and-fractional-parts https://mathgoldmedalist.com/toolkit/vietas-formula https://mathgoldmedalist.com/toolkit/signs-and-roots-of-quadratics https://mathgoldmedalist.com/toolkit/remainder-of-polynomial-division https://mathgoldmedalist.com/toolkit/number-of-positive-divisors https://mathgoldmedalist.com/toolkit/sum-of-positive-divisors https://mathgoldmedalist.com/toolkit/product-of-positive-divisors https://mathgoldmedalist.com/toolkit/general-solutions-of-trig-equations https://mathgoldmedalist.com/toolkit/trigonometric-transformations https://mathgoldmedalist.com/toolkit/trigonometric-identities https://mathgoldmedalist.com/toolkit/trig-sum-to-product https://mathgoldmedalist.com/toolkit/trig-product-to-sum https://mathgoldmedalist.com/toolkit/dual-pythagorean-theorem https://mathgoldmedalist.com/toolkit/angle-bisector-theorem https://mathgoldmedalist.com/toolkit/partial-fraction-decomposition https://mathgoldmedalist.com/toolkit/n-equations-n-variables-probability https://mathgoldmedalist.com/toolkit/adjacency-in-permutations https://mathgoldmedalist.com/toolkit/divisibility-definition-and-properties https://mathgoldmedalist.com/toolkit/modular-arithmetic-definition-and-properties https://mathgoldmedalist.com/toolkit/logarithms-definition-and-properties https://mathgoldmedalist.com/toolkit/two-approaches-to-logarithm-problems https://mathgoldmedalist.com/toolkit/principle-of-inclusion-exclusion https://mathgoldmedalist.com/toolkit/eulers-totient-function https://mathgoldmedalist.com/toolkit/eulers-theorem https://mathgoldmedalist.com/toolkit/graphing-functions-transformations https://mathgoldmedalist.com/toolkit/area-and-geometry-formulas https://mathgoldmedalist.com/toolkit/shoelace-theorem https://mathgoldmedalist.com/toolkit/gauss-rainbow-idea https://mathgoldmedalist.com/toolkit/famous-trigonometric-values https://mathgoldmedalist.com/toolkit/law-of-cosines https://mathgoldmedalist.com/toolkit/ptolemys-theorem https://mathgoldmedalist.com/toolkit/angles-in-circles https://mathgoldmedalist.com/toolkit/cyclic-quadrilateral-rules https://mathgoldmedalist.com/toolkit/unit-circle-in-trigonometry https://mathgoldmedalist.com/toolkit/derivative https://mathgoldmedalist.com/toolkit/remainder-rules https://mathgoldmedalist.com/toolkit/casework-most-limiting-case https://mathgoldmedalist.com/toolkit/signs-no-effect-on-parity https://mathgoldmedalist.com/toolkit/trapezoid-draw-altitudes https://mathgoldmedalist.com/toolkit/circles-tangents-radical-axis https://mathgoldmedalist.com/toolkit/square-roots-two-approaches https://mathgoldmedalist.com/toolkit/geometric-probability https://mathgoldmedalist.com/toolkit/stars-and-bars https://mathgoldmedalist.com/toolkit/double-counting https://mathgoldmedalist.com/toolkit/three-approaches-closed-form https://mathgoldmedalist.com/toolkit/triangle-method-coefficient-identities https://mathgoldmedalist.com/toolkit/try-small-examples https://mathgoldmedalist.com/toolkit/three-ideas-in-paths https://mathgoldmedalist.com/toolkit/sin-cos-tan-cot-special-angles https://mathgoldmedalist.com/toolkit/ab-equals-square-or-p-square https://mathgoldmedalist.com/toolkit/calculate-gcd https://mathgoldmedalist.com/toolkit/trig-ratios-right-triangle https://mathgoldmedalist.com/toolkit/substitution https://mathgoldmedalist.com/toolkit/3d-shapes-surface-area-volume https://mathgoldmedalist.com/toolkit/diagonal-of-a-grid https://mathgoldmedalist.com/toolkit/ratios-of-areas https://mathgoldmedalist.com/toolkit/menelaus-theorem https://mathgoldmedalist.com/toolkit/regular-polygons https://mathgoldmedalist.com/problems https://mathgoldmedalist.com/problems/2024-amc-10a-problem-11 https://mathgoldmedalist.com/problems/2022-amc-10-12a-problem-16 https://mathgoldmedalist.com/problems/2021-amc-10-12-a-fall-problem-17 https://mathgoldmedalist.com/problems/2021-amc-10-12a-spring-problem-10 https://mathgoldmedalist.com/problems/2021-amc-10-12a-spring-problem-14 https://mathgoldmedalist.com/problems/2020-amc-10-12a-problem-21 https://mathgoldmedalist.com/problems/2020-amc-10a-problem-14 https://mathgoldmedalist.com/problems/2020-amc-10a-problem-8 https://mathgoldmedalist.com/problems/2020-amc-10a-problem-5 https://mathgoldmedalist.com/problems/2012-amc-10a-problem-22 https://mathgoldmedalist.com/problems/2023-amc-10b-problem-22 https://mathgoldmedalist.com/problems/2023-amc-10b-problem-14 https://mathgoldmedalist.com/problems/2022-amc-10b-problem-17 https://mathgoldmedalist.com/problems/2022-amc-10b-problem-15 https://mathgoldmedalist.com/problems/2022-amc-10b-problem-9 https://mathgoldmedalist.com/problems/2022-amc-10b-problem-21 https://mathgoldmedalist.com/problems/2021-amc-10b-fall-problem-22 https://mathgoldmedalist.com/problems/2021-amc-10b-spring-problem-15 https://mathgoldmedalist.com/problems/2023-amc-12a-problem-12 https://mathgoldmedalist.com/problems/2023-amc-12a-problem-10 https://mathgoldmedalist.com/problems/2023-amc-12a-problem-23 https://mathgoldmedalist.com/problems/2022-amc-12a-problem-21 https://mathgoldmedalist.com/problems/2021-amc-12a-fall-problem-12 https://mathgoldmedalist.com/problems/2021-amc-12a-spring-problem-19 https://mathgoldmedalist.com/problems/2021-amc-12a-fall-problem-19 https://mathgoldmedalist.com/problems/2023-amc-12b-problem-14 https://mathgoldmedalist.com/problems/2022-amc-12b-problem-4 https://mathgoldmedalist.com/problems/2021-amc-12b-fall-problem-13 https://mathgoldmedalist.com/problems/2021-amc-12b-spring-problem-16 https://mathgoldmedalist.com/problems/2021-amc-12b-spring-problem-20 https://mathgoldmedalist.com/problems/2022-amc-8-problem-8 https://mathgoldmedalist.com/problems/2022-aime-ii-problem-10 https://mathgoldmedalist.com/problems/2023-usajmo-problem-1 https://mathgoldmedalist.com/problems/2018-usamo-problem-1 https://mathgoldmedalist.com/problems/2025-mathcounts-chapter-sprint-round-problem-27 https://mathgoldmedalist.com/problems/2025-mathcounts-state-sprint-round-problem-30 https://mathgoldmedalist.com/problems/2025-hmmt-algebra-number-theory-round-problem-7 https://mathgoldmedalist.com/problems/2016-bmo1-2017-problem-3 https://mathgoldmedalist.com/problems/2025-smo-junior-problem-8 https://mathgoldmedalist.com/problems/2025-amc-12b-problem-7 https://mathgoldmedalist.com/problems/2025-smo-open-problem-7 https://mathgoldmedalist.com/problems/2025-amc-10a-12a-problem-18-12 https://mathgoldmedalist.com/problems/2025-amc-10a-12a-problem-23-12 https://mathgoldmedalist.com/problems/2025-amc-12a-problem-19 https://mathgoldmedalist.com/problems/2025-amc-10b-problem-15 https://mathgoldmedalist.com/problems/2025-amc-10b-12b-problem-24-20 https://mathgoldmedalist.com/problems/2025-amc-12b-problem-18 https://mathgoldmedalist.com/problems/2026-aime-ii-problem-9 https://mathgoldmedalist.com/problems/2026-aime-ii-problem-7 https://mathgoldmedalist.com/problems/2026-aime-i-problem-8 https://mathgoldmedalist.com/problems/2026-aime-i-problem-6 https://mathgoldmedalist.com/problems/2026-aime-i-problem-4 https://mathgoldmedalist.com/problems/2026-mathcounts-state-sprint-round-problem-30 https://mathgoldmedalist.com/problems/2026-mathcounts-state-sprint-round-problem-20 https://mathgoldmedalist.com/problems/2026-mathcounts-state-sprint-round-problem-24 https://mathgoldmedalist.com/problems/2026-mathcounts-state-target-round-problem-5 https://mathgoldmedalist.com/problems/2026-mathcounts-state-team-round-problem-7 https://mathgoldmedalist.com/problems/2026-mathcounts-state-countdown-round-problem-78 https://mathgoldmedalist.com/problems/2024-amc-10a-12a-problem-23-17 https://mathgoldmedalist.com/problems/2024-amc-10a-12a-problem-15-9 https://mathgoldmedalist.com/problems/2024-amc-10b-12b-problem-18-14 https://mathgoldmedalist.com/problems/2024-amc-10b-12b-problem-14-9 https://mathgoldmedalist.com/problems/2024-amc-12a-problem-20 https://mathgoldmedalist.com/problems/2024-amc-12a-problem-15 https://mathgoldmedalist.com/problems/2024-amc-12b-problem-15 https://mathgoldmedalist.com/problems/2024-amc-12b-problem-11 https://mathgoldmedalist.com/problems/2024-amc-12b-problem-17 https://mathgoldmedalist.com/problems/2024-amc-12a-problem-19 https://mathgoldmedalist.com/problems/2025-aime-ii-problem-9 https://mathgoldmedalist.com/problems/2025-aime-ii-problem-4 https://mathgoldmedalist.com/problems/2025-aime-i-problem-5 https://mathgoldmedalist.com/problems/2025-aime-i-problem-6 https://mathgoldmedalist.com/problems/2026-mathcounts-chapter-sprint-round-problem-30 https://mathgoldmedalist.com/problems/2026-mathcounts-chapter-sprint-round-problem-28 https://mathgoldmedalist.com/problems/2023-amc-10a-problem-23 https://mathgoldmedalist.com/problems/2023-amc-10a-12a-problem-18-22 https://mathgoldmedalist.com/problems/2023-amc-12a-problem-24 https://mathgoldmedalist.com/problems/2023-amc-12a-problem-20 https://mathgoldmedalist.com/problems/2023-amc-12a-problem-22 https://mathgoldmedalist.com/problems/2023-amc-12a-problem-17 https://mathgoldmedalist.com/problems/2023-amc-10b-12b-problem-25 https://mathgoldmedalist.com/problems/2024-amc-12b-problem-8 https://mathgoldmedalist.com/problems/2024-amc-12a-problem-8 https://mathgoldmedalist.com/problems/2022-amc-12a-problem-16 https://mathgoldmedalist.com/problems/2022-amc-12a-problem-14 https://mathgoldmedalist.com/problems/2022-amc-12a-problem-12 https://mathgoldmedalist.com/problems/2026-mathcounts-chapter-target-round-problem-8 https://mathgoldmedalist.com/problems/2026-mathcounts-chapter-team-round-problem-9 https://mathgoldmedalist.com/problems/2023-amc-12a-problem-19 https://mathgoldmedalist.com/problems/2025-mathcounts-state-sprint-problem-29 https://mathgoldmedalist.com/problems/2025-mathcounts-state-sprint-problem-26 https://mathgoldmedalist.com/problems/2025-mathcounts-state-target-problem-8 https://mathgoldmedalist.com/problems/2025-mathcounts-state-target-problem-6 https://mathgoldmedalist.com/problems/2025-mathcounts-state-team-problem-9 https://mathgoldmedalist.com/problems/2025-amc-8-problem-25 https://mathgoldmedalist.com/problems/2025-amc-8-problem-24 https://mathgoldmedalist.com/problems/2026-amc-8-problem-23 https://mathgoldmedalist.com/problems/2024-amc-8-problem-23 https://mathgoldmedalist.com/problems/2022-promys-problem-5 https://mathgoldmedalist.com/problems/2020-amc-8-problem-21 https://mathgoldmedalist.com/problems/2019-amc-8-problem-25 https://mathgoldmedalist.com/problems/2019-amc-8-problem-24 https://mathgoldmedalist.com/competitions https://mathgoldmedalist.com/competitions/usamo https://mathgoldmedalist.com/competitions/usajmo https://mathgoldmedalist.com/competitions/aime https://mathgoldmedalist.com/competitions/amc-12 https://mathgoldmedalist.com/competitions/amc-10 https://mathgoldmedalist.com/competitions/amc-8 https://mathgoldmedalist.com/resources https://mathgoldmedalist.com/ideas https://mathgoldmedalist.com/about