Proof

(related to Proposition: Congruences and Division with Quotient and Remainder)

"$\Rightarrow$"

"$\Leftarrow$"

Altogether, it follows $a\equiv b(m)\Longleftrightarrow r_a=r_b.$


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References

Bibliography

  1. Landau, Edmund: "Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927
  2. Jones G., Jones M.: "Elementary Number Theory (Undergraduate Series)", Springer, 1998