List questions from contest-math

Published on 12 Apr 2019 - 20:11

90

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A point such that Areas of triangle formed is equal to area of given quadrilateral

Published on 13 Apr 2019 - 13:51

794

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Matrix problem similar to Problem 3, SEEMOUS 2019

Published on 25 Mar 2026 - 18:45

133

Views

A constraint that implies convexity

Published on 25 Mar 2026 - 6:39

144

Views

Proving the independence of an equation, from certain variables

Published on 28 Mar 2026 - 7:44

50

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Minimizing lengths of cevians in an isosceles right triangle

Published on 29 Mar 2026 - 8:20

159

Views

Why is this proof of a congruence relation valid?

Published on 16 Apr 2019 - 23:58

131

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Find the numbers of ordered array $(a,b,c,d)$ such $a^2+b^2\equiv c^3+d^3\pmod p$

Published on 17 Apr 2019 - 15:33

76

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If $a^3-b^3\equiv 0\bmod3$ prove that $a^3-b^3\equiv 0\bmod 9$

Published on 28 Mar 2026 - 7:45

72

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A question from a past BMO exam, on modulo

Published on 28 Mar 2026 - 7:43

665

Views

Suppose $f : [0, 1] \to [0, 1]$ is differentiable such that $|f'(x)|\ne1$ for all $x\in[0, 1]$. Prove $\exists !a,b\in[0,1]:f(a)=a,f(b)=1-b$

Published on 18 Apr 2019 - 23:07

272

Views

A problem about the field of rational functions over finite field

Published on 28 Mar 2026 - 8:33

104

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If $f(x)f(y)+f(xy)\le -\frac{1}{4},\forall x,y\in[0,1)$, show that $f(x)=-\frac{1}{2}$

Published on 27 Mar 2026 - 5:41

1k

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finding a tangent line to a parabola

Published on 25 Apr 2019 - 0:10

5.4k

Views

Math contest problem about 2 trains leaving the same station at different times

Published on 25 Apr 2019 - 18:24

List Question

$4^x + 5^x = 6^x$

A point such that Areas of triangle formed is equal to area of given quadrilateral

Matrix problem similar to Problem 3, SEEMOUS 2019

A constraint that implies convexity

Proving the independence of an equation, from certain variables

Minimizing lengths of cevians in an isosceles right triangle

Why is this proof of a congruence relation valid?

Find the numbers of ordered array $(a,b,c,d)$ such $a^2+b^2\equiv c^3+d^3\pmod p$

If $a^3-b^3\equiv 0\bmod3$ prove that $a^3-b^3\equiv 0\bmod 9$

A question from a past BMO exam, on modulo

Suppose $f : [0, 1] \to [0, 1]$ is differentiable such that $|f'(x)|\ne1$ for all $x\in[0, 1]$. Prove $\exists !a,b\in[0,1]:f(a)=a,f(b)=1-b$

A problem about the field of rational functions over finite field

If $f(x)f(y)+f(xy)\le -\frac{1}{4},\forall x,y\in[0,1)$, show that $f(x)=-\frac{1}{2}$

finding a tangent line to a parabola

Math contest problem about 2 trains leaving the same station at different times

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