Question

Number Theory: In the process of calculating the Jacobi Symbol of (107/137), I get +(-1)(15/107), which I evaluate to -(15/107). Well it turns out that the right evaluation of this step is +(15/107) and checking with the book and a quick program I wrote yields that 107 is indeed a square (mod 137). Please explain what's the reasoning behind that particular step?

Answer 1

will solve it ltr

Answer 2

lol okay thanks

Answer 3

btw there was a typo there, I meant "Jacobi Symbol" not "Jacobian Symbol" haha

Answer 4

haha xD ok lol i think i have one mnt :P
the idea is by finding x , in

107=x^2 mod 137

x=137n+92
x=137n+45

chose n=0 , x=92 for example
thus
92^2=107 mod 137

Answer 5

its ok i got what u mean :P

Answer 6

yup that's probably true, but I'm concerned with the calculation of the Jacobi symbol itself, not the actual calculation of the square root. 137 is not a 3 (mod 4) prime so I'm not interested in computing x^2 = 107 (mod 137) hahaha

Answer 7

then whats ur question :O

Answer 8

ur not looking for positive or negative , then what ?

Answer 9

I was asking about that step in computing the jacobi symbol of (107/137), not solving x^2 = 107 (mod 137). Sorry if my original post was confusing?

Answer 10

oh ok :P
btw how did u get the 15/107 part ?

Answer 11

cuz 137 is prime , thus
it would be the same as legendre symbol hence its +1

Answer 12

or r u trying to show that both
(15/137)=(107/137 ) ?

Answer 13

137 is prime , thus
a/137= +1 all the time :O

Answer 14

(15/107) is an intermediate step when you're trying to evaluate (107/137) for its Jacobi Symbol hehe