## sauravshakya Group Title Just for fun: x^7 = y^2-713 where x and y are prime numbers. Find all the solution of x and y. one year ago one year ago

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

2. sauravshakya Group Title

Nope. Find all possible values.

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

4. sauravshakya Group Title

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

5. sauravshakya Group Title

That will help.

6. mukushla Group Title

im watching :)

7. ganeshie8 Group Title

$$y = \sqrt{x^7 + 713}$$ 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)

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

9. shubhamsrg Group Title

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

10. ganeshie8 Group Title

i felt this one tough :)

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 Group Title

@sauravshakya how can we say that ?

13. sauravshakya Group Title

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

14. sauravshakya Group Title

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

15. shubhamsrg Group Title

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