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Proposition: Legendre Symbols of Equal Residues

Let $p > 2$ be a prime number. If two integers $n,m\in\mathbb Z$ belong to the same congruence classes modulo $p$ then their Legendre symbols modulo $p$ are equal, formally $$n(p)\equiv m(p)\Longrightarrow \left(\frac np\right)=\left(\frac {m}p\right).$$

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Proofs: 1

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Proofs: 1
Solutions: 2

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References

Bibliography

  1. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927