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A brain teaser like number theory problem
9:51
A brain teaser like number theory problem
Can an irrational number be raised to an irrational power be rational?
0:36
Can an irrational number be raised to an irrational power be rational?
Can you solve this sequence problem from IMO 1986 Short List
11:45
Can you solve this sequence problem from IMO 1986 Short List
Can you solve this Olympiad problem from Austria 2005?
7:44
Can you solve this Olympiad problem from Austria 2005?
Find the minimum value of sqrt(x^2+y^2) if 5x+12y=60
7:41
Find the minimum value of sqrt(x^2+y^2) if 5x+12y=60
[IMO-1981] Find f(3, 2023) when f(x, y) satisfy certain rules
13:10
[IMO-1981] Find f(3, 2023) when f(x, y) satisfy certain rules
Find the value of an expression of a, b, c, when they are roots of P(x)=x^3-2007x+2002
3:53
Find the value of an expression of a, b, c, when they are roots of P(x)=x^3-2007x+2002
What is the probability of answering this correctly?
12:54
What is the probability of answering this correctly?
If ab+bc+ac=0, calculate a^2/(a^2+2bc)+b^2/(b^2+2ac)+c^2/(c^2+2ab)
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If ab+bc+ac=0, calculate a^2/(a^2+2bc)+b^2/(b^2+2ac)+c^2/(c^2+2ab)
Find an irrational number a, such that a^2+2a and a^3-6a are both rational
5:48
Find an irrational number a, such that a^2+2a and a^3-6a are both rational
Find the real roots of equation (97-x)^(1/4)+x^(1/4)=5
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Find the real roots of equation (97-x)^(1/4)+x^(1/4)=5
How to solve a cubic equation?
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How to solve a cubic equation?
What can you get from 1/a+1/b+1/c=1/(a+b+c)
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What can you get from 1/a+1/b+1/c=1/(a+b+c)
Find a six-digit number x, such that 2x, 3x, 4x, 5x, 6x all contain the same digits in x.
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Find a six-digit number x, such that 2x, 3x, 4x, 5x, 6x all contain the same digits in x.
Prove that 8p-1 is a composite number when p and 8p+1 are both prime
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Prove that 8p-1 is a composite number when p and 8p+1 are both prime
If x+y+z=0, prove that x^3+y^3+z^3=3xyz
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If x+y+z=0, prove that x^3+y^3+z^3=3xyz
Find a_2023 if a_{n+2}=(1+a_{n+1})/a_n
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Find a_2023 if a_{n+2}=(1+a_{n+1})/a_n
Solve this equation system
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Solve this equation system
When a+b+c=0, calculate the value of this expression
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When a+b+c=0, calculate the value of this expression
Prove that 1/2+1/3+..+1/n is not an integer
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Prove that 1/2+1/3+..+1/n is not an integer
Calculate sum{sqrt[1+i^(-2)+(i+1)^(-2)]}
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Calculate sum{sqrt[1+i^(-2)+(i+1)^(-2)]}
Prove that the integer part of (2+sqrt3)^n is odd
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Prove that the integer part of (2+sqrt3)^n is odd
[Corrected] Solve equation: x^2+[x]=3
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[Corrected] Solve equation: x^2+[x]=3
Prove [x]+[x+1/n]+..+[x+(n-1)/n]=[nx]
8:56
Prove [x]+[x+1/n]+..+[x+(n-1)/n]=[nx]
Solve equation: x^2+[x]=3
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Solve equation: x^2+[x]=3
Solve equation: x^3+[x]=3
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Solve equation: x^3+[x]=3
Factorize (ab-1)(a+b)^2+1
5:45
Factorize (ab-1)(a+b)^2+1
Solve for distinct natural number of x,y, such that x^y = y^x
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Solve for distinct natural number of x,y, such that x^y = y^x
Solve x in sqrt(x+2sqrt(x+...+2sqrt(x+2sqrt(3x))))=x
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Solve x in sqrt(x+2sqrt(x+...+2sqrt(x+2sqrt(3x))))=x
Prove 1/(n+1) + 1/(n+2) + ... + 1/(3n+1) is between 1 and 2
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Prove 1/(n+1) + 1/(n+2) + ... + 1/(3n+1) is between 1 and 2