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Proof

(related to Proposition: Diophantine Equations of Congruences)

• By definition, every Diophantine equation $f(x_1,\ldots,x_r)$ is a sum of terms and each term is a product of one or more powers of the variables $x_1,\ldots,x_n.$
• The claim now follows immediately from the corollary sums, products, and powers of congruences modulo the positive integer $m.$
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References

Bibliography

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