Math problem of the week #78

Posted on May 20, 2012 by Ricardo Rios

Show that if ab=0 then a=0 or b=0

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Math problem of the week #77

Posted on May 13, 2012 by Ricardo Rios

Show that

1^{-1}=1
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Math problem of the week #76

Posted on May 6, 2012 by Ricardo Rios

Show that

-a-b=-(a+b)
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Math problem of the week #75

Posted on April 29, 2012 by Ricardo Rios

Show that

-0=0
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Math problem of the week #74

Posted on April 22, 2012 by Ricardo Rios

Show that

A \subset B if and only if A - B = \emptyset
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Math problem of the week #73

Posted on April 15, 2012 by Ricardo Rios

Show that a positive integer n can not have a rational square root unless n is a perfect square.

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Math problem of the week #72

Posted on March 18, 2012 by Ricardo Rios

Show that there is not rational number whose cube is 2.

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Math problem of the week #71

Posted on March 11, 2012 by Ricardo Rios

Show that there is not rational number whose square is 3.

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Math problem of the week #70

Posted on March 4, 2012 by Ricardo Rios

For which natural number n do there exist n natural numbers a_{i} ( 1 \le i \le n ) such that \sum_{i=1}^{n} a_{i}^{-2} = 1 ?

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Math problem of the week #69

Posted on February 5, 2012 by Ricardo Rios

If p is a prime number greater 2 and a , b , c integers not divisible by p , prove that the equation

ax^{2}+by^{2} = pz + c

has a integer solution.

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