I am trying to show that x^2 == 25(mod 997) has a solution, but I can't seem to get there.

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- March 30th 2010, 10:52 AMtarheelbornEuler's Criterion
I am trying to show that x^2 == 25(mod 997) has a solution, but I can't seem to get there.

- March 30th 2010, 11:56 AMBlack
x=5?

- March 30th 2010, 12:00 PMtarheelborn
Yeah, thanks. Caught onto that after I belatedly realized that 997 is prime. Thank you!

- March 30th 2010, 12:12 PMBruno J.
- March 30th 2010, 12:50 PMtarheelborn
But since 997 is prime, wouldn't Lagrange's theorem apply to show that there are ONLY 2 solutions?

- March 30th 2010, 01:51 PMtonio
- March 30th 2010, 01:57 PMtarheelborn