Math Problem of the Week Forum

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Undergrad What is the solution to POTW #281 - Oct 30, 2018?
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Undergrad How to Submit Solutions for POTW #330?
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High School Can You Solve This Challenging System of Real Number Equations?
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High School How to Solve a Logarithmic Equation?
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High School How to Prove Sin Equations with Given Constraints?
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Undergrad Is Any Subgroup of a Finite Group with Smallest Prime Order Divisor Normal?
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Undergrad Is $f$ a proper map if the fibers are compact?
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High School Can You Solve This Triangle Cotangent Ratio Problem?
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Undergrad Is a dense, locally compact subspace always open in a compact Hausdorff space?
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High School How Do You Solve for \(x^4 + y^4\) Given These Equations?
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Undergrad Can an entire function with a specific limit at infinity be non-constant?
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Undergrad Why can't $u$ achieve its maximum in the interior of $\Omega$?
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High School How Does Cyclic Product Change for Polynomial Roots?
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Undergrad Is a Uniformly Convergent Sequence of Bounded Functions Also Bounded?
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High School Real Numbers and Proportional Relationships: Solving for x, y, and z | POTW #333
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Undergrad How many subspaces can be formed in a vector space over a finite field?
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Undergrad Let $(X_n)_{n \in \Bbb N}$ be a sequence of positive i.i.d. random variables
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Undergrad Is the Quotient of a Banach Space by a Closed Linear Subspace also Banach?
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When Is \( n^4 + 4 \) a Prime Number?
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Undergrad Problem Of The Week # 323 - Sep 14, 2018
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The Problem of the Week #331: How do you integrate the arcsine squared function?
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Undergrad Are There Infinite Primes of the Form 4k + 1?
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Undergrad Is Every Cofibration Injective?
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Prove the Identity: sin(2x) + sin(2y) + sin(2z) = 4sin(x)sin(y)sin(z)
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Undergrad How Do Nonempty Closed Sets Intersect in Compact Spaces?
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Can Ceva's Theorem Solve the Triangle Concurrency in POTW #329?
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Undergrad Can You Crack This Vector Identity Challenge?
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High School Minimum Natural Number for Fraction Expression #328 Aug 24, 2018 POTW
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Undergrad What is the order of $SL_n(\Bbb F_p)$ for a prime integer $p$?
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Undergrad Countable Dense Open Sets in Compact Hausdorff Spaces?
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Undergrad What is the Sum of a Series Involving Sine Squared for $0 < x < \pi$?
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High School How Can You Prove That 83 Divides x in This Mathematical Series?
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High School Find the Number of Polynomials with Coefficients in {0-9} That Satisfy P(-1)=-9
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Undergrad How can you prove the number-theoretic equation $\sum_{d|n} \phi(d) = n$?
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High School Can You Prove e^x Is Greater Than x^2 for All Positive x?
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Undergrad Is the adjunction space $X \cup_f Y$ normal for closed $A$ and continuous $f$?
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Undergrad What is the Solution to POTW #317?
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High School What Is the Missing Digit in \(1995^{10}\)?
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Undergrad Can You Prove This Advanced Mathematical Inequality?
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High School How Do You Solve This Complex Integral Problem?
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Undergrad Is $f$ Constant if Distance Between Points is Raised to a Power Greater than 1?
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High School Probability of Satisfying Floor Inequality with Random Real Numbers
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Undergrad How can a rank 1 complex matrix be written as a product of two matrices?
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Undergrad Why is the Kernel of the Evaluation Map Principal?
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High School How to Solve for Unknown Variables with Given Equations?
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Undergrad Is the direct sum of isomorphic commutative rings always equal in size?
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High School How Can You Prove a Quadratic with No Real Roots Satisfies the Inequality?
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Undergrad What is the solution to the nonlinear differential equation?
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Undergrad Can Two Solutions of a PDE be Equal with Given Boundary Conditions?
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High School What Is the Missing Digit in $2^{29}$?
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High School Probability of Hitting Center of a Square Target - POTW #318 (Jun 13, 2018)
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Undergrad What is the Average Value of |dφ/dz|^2 over the Open Unit Disk?
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What is the volume of a pyramid with given side lengths?
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High School Can You Discover the Integer Pair That Satisfies This Unique Sum Equation?
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High School Can This Complex Integral Be Proven Rational?
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Can any two bounded functions be transformed into a maximum of two functions?
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High School Are There Limited Ordered Triples for Complex Number Equations?
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Undergrad What is Jacobi's identity for Lie derivatives on a smooth manifold?
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High School Can Complex Equation |z|=1 Be Proven for 11z^10+10iz^9+10iz-11=0?
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Given $n$ points in the plane, any listing (permutation) $p_1, p_2,\dots,p_n$
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Undergrad Is the Integral of an Analytic Function on a Closed Contour Purely Imaginary?
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High School Can Exponents Reveal Which Fraction is Greater?
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What values of alpha make these curves tangent?
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How Does Air Resistance Affect a Fire Helicopter's Bucket?
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What Is the Probability John Gets More Heads Than Mary?
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Electric Field Zero: Charge Distribution on Y-Axis
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Choosing the Right Force: Bug Survival Odds on a Frictionless Table
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Undergrad How can we show that $D_n(t)$ has a bounded integral over a certain interval?
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What is the largest possible radius of a circle contained in a $4$-dimensional hypercube of side length $1?$
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What Power is Needed for Sinusoidal Waves in a Taut Rope?
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Problem Of The Week # 305 - Apr 10, 2018
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High School Can You Prove This Factorial Inequality for All Positive Integers?
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Can one choose a winning team from each day in a round-robin tournament with no repeats?
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High School Probability of Midpoint in Set S | POTW #307 Mar 28th, 2018
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Undergrad How Do You Solve This Integral for Positive Integer n?
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Find the locus of a point moving so that the sum of its perpendicular distances from the four lines is constant
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High School Is \(n^{n+1} > (n+1)^n\) for All \(n \geq 3\)?
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If $k$ is large, the expression above is approximately $\frac{1}{3}$.
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High School What Is the Minimum Sum of $a+b+c+d+e+f+g$ Given Their Progressive Inequalities?
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Undergrad Is $\Bbb Z\otimes_{\Bbb Z} \Bbb R$ isomorphic to $\Bbb C$?
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Is the Area and Radius of a Triangle Always Proportional to its Side Lengths?
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High School How Do You Solve Complex Series Without a Calculator?
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High School What is the Minimum Value of Sum of Squares for Real Numbers in this POTW?
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Can you find the limit of a complex function containing integrals and exponents?
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Convex Quadrilateral Problem: Prove Inequality with Diagonal Point T
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Undergrad What is the solution to POTW #265 - Feb 13, 2018?
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Are Not More Than 70 Percent of Triangles Acute-Angled?
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Can you solve these quadruple equations with real numbers?
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Undergrad What is the solution to POTW #264 for Jan 23, 2018?
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High School What are the possible values of 1/a + 1/b when a^3+3a^2b^2+b^3 = a^3b^3?
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High School Triangle ABC: Prove cot(A/2) + cot(C/2) = 2cot(B/2)
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Odd Prime Factor of \( a_{2015} \)?
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High School What is the sum of the angles in a right triangle?
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When Is \( (k+1)^n+(k+2)^n+(k+3)^n+(k+4)^n+(k+5)^n \) Divisible by 5?
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High School What Is the Product of (1+k) for All Roots of a 15th Degree Polynomial?
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Undergrad Is the Real Projective Plane's Gaussian Curvature Always Positive?
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Is $h(x)$ a linear polynomial?
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High School What Is the Smallest Integer $a$ for $\frac{1}{640}=\frac{a}{10^b}$?
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Is Triangle ABC a Right-Angled Triangle in Tetrahedron OABC?
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High School How to Maximize the Product ab Given Specific Square Root Conditions?
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