## anonymous 4 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.

1. anonymous

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

2. anonymous

Nope. Find all possible values.

3. anonymous

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

4. anonymous

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

5. anonymous

That will help.

6. anonymous

im watching :)

7. 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)

8. anonymous

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

9. shubhamsrg

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

10. ganeshie8

i felt this one tough :)

11. anonymous

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

@sauravshakya how can we say that ?

13. anonymous

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

14. anonymous

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

15. shubhamsrg

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