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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 $$n(p)\equiv m(p)\Longrightarrow \left(\frac np\right)=\left(\frac {m}p\right).$$

| | | | | created: 2019-05-12 18:50:27 | modified: 2019-05-12 18:53:07 | by: bookofproofs | references: [1272]

1.Proof: (related to "Legendre Symbols of Equal Residues")

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Bibliography (further reading)

[1272] Landau, Edmund: “Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927