The name is absent



c22

Further, we have

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

≥ a^+1xn+1 - bn+1

> a~[ xn+1 — b1

> a~[n+1 + ¢(1)) — &i
= a~[y1-b1.

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

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

a~l^xk~k - bk~1 ≥ a^xk~1 - bk.

Hence we have

ak.1yk - bk^1 = a^1(xk~1 + q(k) - bk.1

= a^1xk~1 - bk.1 + a^l-1q(k)

> a[xk~k — bk + a[q(k)

≥ a[(xk~1 + q(k}) - bk
= akyk-bk.

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

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

O.nX b∏ ≥           ¼ι+l∙

We have

a∏yn+1-bn = ɑɪ(æ1 - q(n}) - bn

≥ dn+ιX1 - bn+ι -aτnq(π)

> aτn+1x1 - bn+1 - a^+1q(n)

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



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