Legendre Symbol
Source: Iran TST 2004
January 9, 2009
modular arithmeticquadraticsspecial factorizationsnumber theory proposednumber theory
Problem Statement
Suppose that is a prime number. Prove that for each , there exists an such that:
\left(\begin{array}{c}n\\ \hline p\end{array}\right)\equal{}\left(\begin{array}{c}n\plus{}k\\ \hline p\end{array}\right)