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henpen

Is this true: 'The only way you can get from one perfect square, q^2, to another, p^2, by multiplying by a constant [i.e. p^2=a^2 q^2] is if q IS that factor [i.e. q^2=a^2]'?

  • one year ago
  • one year ago

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  1. hartnn
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    'the first square IS that factor' what is 'that' here? factor of whose ? \(b^2=ma^2\)

    • one year ago
  2. henpen
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    \[q^2=49p^2\]Must \[q=49\]?

    • one year ago
  3. henpen
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    I've edited it. Is that still ambiguous?

    • one year ago
  4. hartnn
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    then i don't think its always true.... q equal 49, is not necessary

    • one year ago
  5. henpen
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    Of course apart from the trivial case where p=1

    • one year ago
  6. henpen
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    Counterexample: 6^2= 4 * 2^2 Damn, it's wrong!

    • one year ago
  7. hartnn
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    yea, its false....

    • one year ago
  8. henpen
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    This popped up in http://www.komal.hu/verseny/feladat.cgi?a=honap&h=201210&t=mat&l=en if anyone's interested...

    • one year ago
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