PROOF 78

Prove.

The repetend is shorter than the denominator

On the rational numbers ℚ.

Definition D1

For a natural number q ≥ 2 and an integer p with 0 ≤ p < q, set r₀ = p, and for each k ≥ 0 determine dₖ₊₁ and rₖ₊₁ by 10rₖ = q·dₖ₊₁ + rₖ₊₁, 0 ≤ rₖ₊₁ < q. Call dₖ the k-th digit of p/q after the decimal point.

Proof.

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