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- anonymous

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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- anonymous

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

- katieb

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- anonymous

Is there a range for this? (though I guess not, most of these question have set ansers)

- anonymous

Nope. Find all possible values.

- anonymous

X=2 and Y=29... though I'll want to learn the legitimate mathematical solution...lol

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- anonymous

when y is even x is odd
when y is odd x is even.

- anonymous

That will help.

- anonymous

im watching :)

- 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

Nice! right. there's only one even prime...;lol

- shubhamsrg

but how can we say when y is even x is odd
when y is odd x is even. ?

- ganeshie8

i felt this one tough :)

- 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

@sauravshakya how can we say that ?

- anonymous

When y is even y^2 is also even and 713 is odd.
And odd + even is odd

- anonymous

When y is odd , y^2 is also odd and 713 is also odd.
And 0dd + odd is even.

- shubhamsrg

hmmm...that was really stupid of me to ask.. nice..

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