anonymous
  • anonymous
Just for fun: x^7 = y^2-713 where x and y are prime numbers. Find all the solution of x and y.
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Is there a range for this? (though I guess not, most of these question have set ansers)
anonymous
  • anonymous
Nope. Find all possible values.
anonymous
  • anonymous
X=2 and Y=29... though I'll want to learn the legitimate mathematical solution...lol

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anonymous
  • anonymous
when y is even x is odd when y is odd x is even.
anonymous
  • anonymous
That will help.
anonymous
  • anonymous
im watching :)
ganeshie8
  • ganeshie8
\(y = \sqrt{x^7 + 713}\) 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)
anonymous
  • anonymous
Nice! right. there's only one even prime...;lol
shubhamsrg
  • shubhamsrg
but how can we say when y is even x is odd when y is odd x is even. ?
ganeshie8
  • ganeshie8
i felt this one tough :)
anonymous
  • anonymous
quote @ganeshie8 : 'clearly y > 2, so y is odd prime.' lol bruteforcing with a program is really stupid come to think of it.
shubhamsrg
  • shubhamsrg
@sauravshakya how can we say that ?
anonymous
  • anonymous
When y is even y^2 is also even and 713 is odd. And odd + even is odd
anonymous
  • anonymous
When y is odd , y^2 is also odd and 713 is also odd. And 0dd + odd is even.
shubhamsrg
  • shubhamsrg
hmmm...that was really stupid of me to ask.. nice..

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