- #1

Math100

- 783

- 220

- Homework Statement
- Without evaluating the Legendre symbols, prove that ## 1(1|73)+2(2|73)+3(3|73)+\dotsb +72(72|73)=0 ##. (Hint: As ## r ## runs through the numbers ## 1, 2, ..., 72 ##, so does ## 73-r ##.)

- Relevant Equations
- Let ## p ## be an odd prime. Then ## \sum_{r=1}^{p-1}r(r|p)=0 ## if ## p\equiv 1\pmod {4} ##.

Since ## p=73 ## in this problem, how should I prove that ## \sum_{r=1}^{73-1}r(r|73)=0 ##? Given that ## 73=1\pmod {4} ##.