The name is absent

^c22

Further, we have

α!₊ιJ∕¹ - b_n+1 = a^₊₁(xⁿ⁺¹ + q(1)) - b_n+1

≥ a^₊₁xⁿ⁺¹ - b_n+1

> a~[ xⁿ⁺¹ — b₁

> a~[ (æⁿ⁺¹ + ¢(1)) — &i
= a~[y¹-b₁.

It means that l(y¹) ψ 1. It is a contradiction.

(2). If 1 < к < n + 1, then y^k = x^k~^k ⅛ q(k'). Since l(x^k~^r) = к — 1, it implies
that

a~l^x^k~^k - b_k~₁ ≥ a^x^k~¹ - b_k.

Hence we have

a_k.₁y^k - b_k^₁ = a^₁(x^k~¹ + q(k∖) - b_k.₁

= a^₁x^k~¹ - b_k.₁ + a^l-₁q(k)

> a[x^k~^k — b_k + a[q(k)

≥ a[(x^k~¹ + q(k}) - b_k= ^aky^k-b_k.

It means that l(y^k) ψ k. It is again a contradiction.

(3). If к = n + 1, then y^n+k = x¹ — q(∏). Notice that

O._nX b∏ ≥ ¼ι+l∙

We have

^a∏yⁿ⁺¹-b_n = ɑɪ(æ¹ - q(n}) - b_n

≥ dn+ιX¹ - b_n+ι -a^τ_nq(π)

> a^τ_n+1x¹ - b_n+1 - a^₊₁q(n)

= an+ι(χ¹ - q(ⁿ∖) - b_n+ι
= a^₊₁yⁿ⁺¹ - b_n+1.