Math Problem of the Week Forum

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High School Can $2^{\sqrt{12}}$ Exceed 11?
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High School What is the Range of $w(w+x)(w+y)(w+z)$ When $x+y+z+w=x^7+y^7+z^7+w^7=0$?
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High School Can Both Solutions of This Quadratic Equation Be Perfect Squares?
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High School How many positive integral solutions $(x,\,y)$ are there for the equation $\dfrac{1}{x+1}+\dfrac{1}{y}+\dfrac{1}{y(x+1)}=\dfrac{1}{2015}$?
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High School What is the greatest 5-digit palindrome for 7n to be a 6-digit palindrome?
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High School How do you solve a system of equations with rational functions?
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High School Prove $0\le xy+yz+zx-2xyz\le7/27$ for $x+y+z=1$
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High School Can You Simplify This Trigonometric Expression?
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High School How Does Solving P(x) Influence Q(x^2)?
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High School Can You Prove This Inequality with Positive Real Numbers?
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High School How Do You Evaluate the Product of g(x) at the Roots of a Quintic Polynomial?
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High School Sum of Cosine Values for $x$ | POTW #480 8/24/2021 | $100^{\circ}<x<200^{\circ}$
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High School What is the value of (x+y)(y+z)(z+x) if 1/(x+y+z) = 1/x + 1/y + 1/z?
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Undergrad Can a Finite Measure Space Have Uncountably Many Positive Measure Members?
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Undergrad Is Function $f$ Convex if its Hessian Matrix is Positive Semidefinite?
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High School Find All Positive Integer Pairs for (x, y) in sqrt[3]{7x^2-13xy+7y^2}=|x-y|+1
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High School How to Evaluate the Expression for Roots of the Polynomial in POTW #476?
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High School What is the solution for evaluating $ab+cd$ with given constraints in POTW #477?
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High School Can You Solve This Unique Fraction Challenge?
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High School Can you solve this week's POTW #474: Four real numbers with unique permutations?
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High School What Is the Largest Natural Number $n$ Such That $2^n$ Divides $3^{2016}-1$?
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High School Discover the Area of Points in a Unit Square | POTW #471
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High School How Many Integer Solutions Exist for the Equation |x|+|y|+|z|=2010?
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Undergrad What is the Unique Linear Functional in $M_n(\Bbb F)$ Satisfying Two Conditions?
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High School Prove Inequality: Integral of Square Root vs. Trigonometric Function
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High School Find Functions Satisfying $f^d(x)=2015-x$ for All Divisors of 2015
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High School Can $(n^2+11n-4) \cdot n! + 33 \cdot 13^n + 4$ Be a Perfect Square?
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High School What is the Time Estimate for Completing a 1000-Piece Jigsaw Puzzle?
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High School Finding Extremes of x^3+y^3+z^3+xyz for Real Numbers with Constraints
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High School Can You Solve This Week's Challenging System of Equations?
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High School Which Prime Numbers Make $2p^3 + 4p^2 - 3p + 12$ a Fifth Power?
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High School Is Every Positive Real Number a Solution to (x+1)(x+2)(x+5)≥36x?
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Undergrad Nontrivial Normal Subgroup in Finite Groups with Index Constraints?
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Undergrad How to prove the convergence of a series with absolute values?
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High School What Are the Possible Values of c for a Triangle with Area 5?
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High School Can All Outputs of a Quadratic Function Be Integers?
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High School Can Non-zero Polynomials with Real Coefficients Have Real Roots in Common?
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High School Is it possible to find 6-digit numbers with a sum of 8?
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High School Possible Values: $f(8765)-f(4321)$ for Functions Satisfying Inequalities
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High School How Do You Solve POTW #456 for (x+20)(y+20)(z+20)?
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High School Can You Solve the Integer System xz-2yt=3 and xt+yz=1?
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High School What is the Greatest Value of an Expression with Given Numbers and Equation?
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High School Integer Solutions for Equation: POTW #453 - Feb 1st, 2021
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High School Can You Solve This Integer Equation for January 25th, 2021?
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High School How Many Divisors of $30^{2003}$ Are Not Divisors of $20^{2000}$?
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High School What are the solutions to x^3+3367=2^n?
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High School Triangle ABC: Find Possible Values of Cos A | POTW #449 Jan 4th 2021
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High School How to Tackle the Latest POTW Inequality Challenge?
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Undergrad Can a Non-Surjective Smooth Harmonic Function on $\Bbb R^2$ Be Non-Constant?
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High School Can You Solve for a and b in This Trigonometric Equation?
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High School Triangle with Complex Number Vertices SATISFIES Equilateral Relation
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High School Proof of Regular Heptagon Ratio: AD^3/AB^3 - (AB+2AC)/(AD-AC) = 1
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High School Maximum Value of Square Root Expression with Three Variables in [0,1]
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High School How Many Non-Congruent Triangles with Integer Sides Can a Given Perimeter Form?
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High School Is Sine of x Greater Than or Equal to 2x Over Pi for Angles Up to Pi/2?
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High School Can You Solve the Convex Quadrilateral Angle Mystery?
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High School Can All Roots of This Cubic Equation Be Bounded by 1?
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High School Is the Expression an Integer When Rational Conditions Apply?
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High School Can You Prove These Inequalities for Real Numbers a, b, and c?
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High School What are the solutions to a set of equations involving triple real numbers and specific conditions?
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Undergrad Can You Evaluate This Tricky Improper Integral?
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High School Is It Possible to Prove Real Root Properties in Cubic Equations?
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Undergrad Is $p$ a prime divisor of $\phi(n)$ if $G$ has an element of order $n$?
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Undergrad How Do You Prove a Point is Critical When a Function is Non-Negative Nearby?
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High School What Is the Value of b If All Roots of the Polynomial Are Positive Real Numbers?
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High School Quadratic Polynomial Problem: Proving Equality with Real Numbers
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High School Solution to Problem #433: Proving a+b+c=0 yields 9
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High School How Many Final Points Can Be Reached in a Ten-Step Lattice Walk?
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High School How Do Divisors Relate in POTW #431's Integer Equation?
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High School Which Integers Make All Roots of This Polynomial Integer?
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High School How Do You Calculate the Sum of Sides and Diagonals of a Regular 12-Gon?
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High School How Can a Fifth Degree Polynomial Meet Specific Divisibility Conditions?
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High School Challenge: Find the Positive Integer for $133^5$ + $110^5$ + $84^5$ + $27^5$
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High School The value of $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$ is 1234.
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Undergrad Show that the equation $2a^3 - 7b^2 = 1$ has no solution over the integers
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High School Can You Solve This Complex Radical Equation?
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High School Maximizing a in $ax^3+bx^2+cx+d$ with Constraints | POTW #424 07/06/2020
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High School How to Calculate the Sum of Squares in Complex Equation Systems?
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High School Problem #422: Four Non-Negative Real Numbers and a Unique Condition
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High School What Natural Numbers Solve the Equation from POTW #421?
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High School Find the Sum of Real Numbers Satisfying Equations
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Undergrad Is $K$ Contained in the Center of $G$ if $|K|=5$ and $|G|$ is Odd?
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Undergrad What is the integral of x - sin x over x^3 from 0 to infinity?
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High School What Is the Probability That a Bridge Is Empty at Noon?
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High School Can you solve this week's POTW: Integrating a Complex Expression? May 25th, 2020
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High School Acute Triangle ABC: Point P and Line Intersections Formula
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High School Can You Solve These Unique System of Equations?
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High School How Can One Non-Real Root Be Guaranteed in Equation #416?
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High School Prove: No Real Roots for Polynomial x^4-px^3+qx^2-sqrt(q)x+1
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Undergrad Can You Tackle the Subset Chain Challenge in Math?
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High School Are There Two Integer Solutions to This Quadratic Equation?
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Undergrad Can Harmonic Functions Agree at All Points in a Bounded Domain?
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High School Proving Triangle Inequality for Sides and Opposite Angles in a Triangle
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High School Can Integer Equations Reveal Perfect Square Patterns?
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High School How Do Disjoint Intervals Solve the Inequality in POTW #409?
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High School Minimum Value of $(u-v)^2$ and $\left(\sqrt{2-u^2}-\dfrac{9}{v}\right)^2$
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High School Perfect Squares as Divisors of $1!\cdot 2! \cdot 3! \cdots 9!$
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High School What Is the Smallest n Such That Sequence Sum S_n Exceeds 10000?
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High School Reflection of Parabolas: Find the Sum of Coefficients - POTW #406 Feb 27th, 2020
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High School Find the Smallest Divisible Integer: POTW #405 Feb 20th, 2020
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