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sauravshakya

  • 2 years ago

Just for fun: x^7 = y^2-713 where x and y are prime numbers. Find all the solution of x and y.

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  1. Shadowys
    • 2 years ago
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    Is there a range for this? (though I guess not, most of these question have set ansers)

  2. sauravshakya
    • 2 years ago
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    Nope. Find all possible values.

  3. Shadowys
    • 2 years ago
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    X=2 and Y=29... though I'll want to learn the legitimate mathematical solution...lol

  4. sauravshakya
    • 2 years ago
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    when y is even x is odd when y is odd x is even.

  5. sauravshakya
    • 2 years ago
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    That will help.

  6. mukushla
    • 2 years ago
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    im watching :)

  7. ganeshie8
    • 2 years ago
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    \(y = \sqrt{x^7 + 713}\) x, y both are primes, clearly y > 2, so y is odd prime. since 713 is odd, we need x^7 to be even to make sqrt(x^7+713) become an odd number since x is a prime only way x^7 to be even is x=2 so olny 1 solutution (2, 29)

  8. Shadowys
    • 2 years ago
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    Nice! right. there's only one even prime...;lol

  9. shubhamsrg
    • 2 years ago
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    but how can we say when y is even x is odd when y is odd x is even. ?

  10. ganeshie8
    • 2 years ago
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    i felt this one tough :)

  11. Shadowys
    • 2 years ago
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    quote @ganeshie8 : 'clearly y > 2, so y is odd prime.' lol bruteforcing with a program is really stupid come to think of it.

  12. shubhamsrg
    • 2 years ago
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    @sauravshakya how can we say that ?

  13. sauravshakya
    • 2 years ago
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    When y is even y^2 is also even and 713 is odd. And odd + even is odd

  14. sauravshakya
    • 2 years ago
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    When y is odd , y^2 is also odd and 713 is also odd. And 0dd + odd is even.

  15. shubhamsrg
    • 2 years ago
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    hmmm...that was really stupid of me to ask.. nice..

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