Proof: By Induction

(related to Proposition: Existence of Solutions of an LDE With More Variables)

By hypothesis, $m > 0$ is a given positive integer $a_1,\ldots,a_r,b$ are given integers.

"$\Rightarrow$"

"$\Leftarrow$"


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References

Bibliography

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

Footnotes


  1. Take for $x_1$ any integer representing the congruence class $x(a_2)$ solving the congruence $(a_1x_1)(a_2)\equiv b(a_2)$ and solve the equation for $a_1x_1+a_2x_2=b$ for $x_2.$