Math Problem of the Week Forum

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High School What is the Largest Possible Value of BD in a Cyclic Quadrilateral?
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High School Find the Minimum Values of Monic Quadratic Polynomials - POTW #403 Feb 2nd, 2020
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High School Is ln(2) Greater Than (2/5)^(2/5)?
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High School How Do You Calculate the Total Length of Intervals for x in This Inequality?
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Undergrad Prove the Famous Result: \(\sum_{k = 1}^\infty \frac{1}{k^2} = \frac{\pi^2}{6}\)
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High School What is the Smallest Possible Value of a in This Polynomial Pattern?
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High School How Do Triangle Sides Relate to Acute Angles?
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High School Can You Solve This Sum of Floor Functions Challenge?
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Undergrad How can you evaluate the integral of cosine raised to the fifth power?
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Undergrad What Is the Center of the Ring of All \( n \times n \) Complex Matrices?
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High School What Is the Sum of the Digits of 3n Given These Conditions?
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High School Polynomial $P(x)$ Satisfying $P(k)=2^k$: POTW #396 Dec 9th, 2019
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High School What is the solution for d in a trigonometric equation with multiple terms?
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High School How Can We Prove the Inequality for Polynomial Roots in POTW #394?
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High School Can You Solve This Trigonometric Inequality?
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High School How to Calculate \(a+b+c\) for Equations Sharing Common Real Roots?
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High School Can you solve this inequality involving positive real numbers?
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High School How to solve for x in a nested polynomial equation?
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High School How Many Real Roots Does This Equation Have?
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High School How Can You Factorize the Polynomial (x+1)(x+2)(x+3)(x+6)-3x^2?
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High School Can You Solve This Advanced Algebra Puzzle?
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High School POTW #386: Evaluate (a+b+c)(b+c+d)(c+d+a)(d+a+b) for x^4-7x^3+3x^2-21x+1=0
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High School Can You Solve the Exponential Equation for Integer Triples $(a, b, c)$?
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High School How Do You Solve the Equation \(x^3(x+1) = 2(x+a)(x+2a)\) for Real \(a\)?
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Undergrad How Do Tensor Products Relate to Supports in Algebraic Geometry?
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Undergrad How Can You Prove This Bessel Function Integral Equals 4/3π?
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Undergrad Why Are There an Odd Number of Elements in a Finite Group Where g^3 Equals 1?
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High School What is $a_{1996}$ in this series?
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Undergrad Can compact Hausdorff sets be expanded by open sets?
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High School Inscribed Quadrilateral Perpendicular Bisectors Convergence Theorem
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High School What Are the Non-Negative Integer Solutions to (xy-7)² = x² + y²?
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High School Is There a Rational Multiple for the Product of Sines from 1 to 90 Degrees?
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High School Alternate solution from MegaMoh:
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High School Prove $a+b>c+d$ for Real Numbers with Sine Inequalities
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High School How Do You Factor \(x^8+4x^2+4\) into Non-Constant Polynomials?
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High School Can Polynomial Constraints Determine a Unique Integer Solution?
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High School Can You Evaluate abc in This System of Cubic Equations?
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Undergrad What is the formula for the volume of a solid unit n-sphere in n+1 dimensions?
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Undergrad Is the Tensor Product of Flat Modules Flat?
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High School POTW #374: Finding the 1000th Digit of the Square Root of a Large Number
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High School Is ab+cd Not Prime in This Integer Puzzle?
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High School POTW #372: Solve $4x^6-6x^2+2\sqrt{2}=0$ without a calculator - June 25th, 2019
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High School How Long is Side CD in a Special Trapezium?
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Undergrad Can You Solve This Linear System of ODE with Initial Conditions?
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High School Can You Solve This Cubic and Square Root Equation?
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Undergrad Can You Prove the Limit of Integrals Over Vanishing Measure Sets Is Zero?
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Undergrad Is $g(z)$ holomorphic if $f$ is holomorphic in $G$?
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High School Can Real Roots in a Quadratic Guarantee a Root in a Quartic?
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Undergrad Is $M$ a Finite Metric Space if $BC(M)$ is a Finite Real Vector Space?
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High School Can You Prove $ab\le 1$ Given $(x+a)(x+b)=9$?
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High School Can You Simplify This Complex Square Root Expression?
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High School Maximizing $abcd$ with given constraints - POTW #366 May 14th, 2019
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Undergrad Can a Finite Group Acting on a Set Have No Fixed Points?
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Undergrad Do Complex Plane Medians Intersect at Triangle Centroid?
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High School Proof of Convergence: Nested Radicals with Constant Sum on May 8, 2019
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High School Prove: Sum of Cubed Roots of Trigonometric Expressions Equals Square Root of 9/2
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Undergrad Can You Tackle This Week's Challenging PDE?
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High School How Do You Calculate the Sum of Minimum Values in Polynomials?
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Undergrad Is There a Simple Group of Order $2n$ for Odd $n \geq 3$?
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Undergrad Can You Tackle This Advanced Series Summation Challenge?
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Undergrad Can You Crack the Challenges in POTW #286?
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High School Can You Solve This Real Number System of Equations?
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High School Prove Inequality: (a+2)(b+2) ≥ cd with a^2 + b^2 + c^2 + d^2 = 4
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High School What is the value of $xy+yz+zx$ in a system of equations with real numbers?
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High School Prove $a^2+b^2\ge 8$ for real roots of $x^4+ax^3+2x^2+bx+1=0$
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High School Find the Minimum Non-Zero Value of A^2+B^2+C^2 with Integer Constraints
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Undergrad What Are This Week's Math Challenges in POTW #342?
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High School How Do Floor Functions Affect the Results of Square Roots in Sequence Problems?
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High School Can Trigonometric Identities Simplify This Week's Complex Integral?
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Undergrad How Do You Solve the Integral from POTW #285?
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Undergrad Is Orientability Preserved by Local Diffeomorphisms?
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High School Prove the Sum of Cube Roots of Roots of a Cubic Equation is Zero
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High School POTW #354: Find Possible Value of a-b When $x^2-x-1$ Divides $ax^{17}+bx^{16}+1$
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Undergrad Can You Match Partitions from Set A and Subset B?
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High School How do I solve for non-negative integers x and y?
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Undergrad How Fast Does the Chain Move Off the Table in POTW #339?
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High School Can You Solve This High School Math Series Without a Calculator?
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High School What is the integral of (x^2+1)/(e^x+1) from -1 to 1?
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Undergrad Can an analytic function on the half plane be represented by an integral?
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Undergrad Topological manifolds with boundary of dimensions
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Undergrad How Do You Prove the Inequality Involving Primes and Harmonic Sum for POTW #337?
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High School What is the Value of Angle MBC in the Triangle-Square Configuration?
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High School Is the Number 2 Truly Persistent?
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Undergrad Is the one-point compactification of X-S homeomorphic to X/S?
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High School Is T Always Equal to 2 in the Persistent Number Theorem?
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High School Can AC Be Less Than Twice FG in a Square Geometry Setup?
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Undergrad How to Solve Integral with Parameters a and b in POTW #283?
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Undergrad What is the proof that a commutative ring with prime proper ideals is a field?
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High School Solve Equation for Trigonometric Functions with Integer and Fractional Parts
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High School Problem Of The Week #345 Dec 18th, 2018
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Undergrad How to Derive g(x) from f(x) Using the Möbius Function?
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High School Can You Solve for a, b, and c Given This Challenging Equation?
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High School Can You Prove $\cos(\cos 1) > \sin(\sin(\sin 1))$?
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Undergrad What is the solution to this week's POTW?
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Undergrad Is $H_n(X)$ Torsion Free if $H_{n-1}(X)$ is Torsion Free?
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Undergrad Did Ackbach Solve This Week's Advanced Math POTW Correctly?
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High School Can You Crack This Week's Rational Equation Challenge?
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High School How Do You Calculate the Sum of Cubed Tangents for Angles from 0 to 89 Degrees?
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Undergrad How to Prove the Integral Identity in POTW #331?
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High School Solution for Roots of x^3-7x+7=0: Week #340 Nov 13th, 2018 POTW
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