Question

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

Answer 1

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

Answer 2

Nope. Find all possible values.

Answer 3

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

Answer 4

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

Answer 5

That will help.

Answer 6

im watching :)

Answer 7

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

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)

Answer 8

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

Answer 9

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

Answer 10

i felt this one tough :)

Answer 11

quote　@ganeshie8　: ＇clearly y > 2, so y is odd prime.＇

lol bruteforcing with a program is really stupid come to think of it.

Answer 12

@sauravshakya how can we say that ?

Answer 13

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

Answer 14

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

Answer 15

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