# Thread: Using this info, factor this number

1. ## Using this info, factor this number

880525^2 = 2
2057202^2 = 3
648581^2 = 6
668676^2 = 77
all (mod 2288233)

How would I use this info to factor 2288233.
Now I know I want an x and a y such that x^2 = y^2 mod 2288233.
So should I be trying to express 77 as a combination of the first 3 equations?
Unfortunately that isn't of the form y^2, but instead a^2 + b^2 + c^2...

2. Mm.. well the product of the first two is 6, which is in the third equation..

3. yah I though about just using the first 3 equations but Im not getting an answer to factor.

heres my work:

(880525 x 2057202) mod 2288233 = 2207120
so I would add this number to 648581 since 2207120^2 and 648581^2 both = 6mod2288233.
Now I find the gcd(2855701, 2288233)
?

*after further investigation, 2207120^2 does NOT equal 6 mod 2288233.
Can someone help me with this?

4. Originally Posted by chrisc
yah I though about just using the first 3 equations but Im not getting an answer to factor.

heres my work:

(880525 x 2057202) mod 2288233 = 2207120 I suspect that you are on the right lines, and that this last number should actually be 2207124. Then everything seems to work well.
so I would add this number to 648581 since 2207120^2 and 648581^2 both = 6mod2288233.
Now I find the gcd(2855701, 2288233)
?

*after further investigation, 2207120^2 does NOT equal 6 mod 2288233.
Can someone help me with this?
..

5. thank you. so I was able to solve this using only the first 3 equation.