Question

Prove the uniqueness of the quotient-remainder theorem. That is, if a and d are integers with d>0 and if q₁, r₁, q₂, and r₂ are integers such that a = d q₁ + r₁ where 0 ≤ r₁ < d and a = d q₂ + r₂ where 0 ≤ r₂ < d, then q₁ = q₂ and r₁ = r₂.