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Corrigendum to the paper: “On some new congruences between generalized Bernoulli numbers II”

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THÉORIE DES NOMBRES BESANÇON

Années 1992/93-1993/94

Corrigendum to the paper

"On some new congruences between generalized Bernoulli numbers, II"

(Publ. Math. Fac. Sci. Besançon (Théorie des Nombres) Années 1989/90 - 1990/91)

J. URBANOWICZ

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Corrigendum to the paper

"On some new congruences between generalized Bernoulli numbers, II"

(Publ. Math. Fac. Sci. Besançon (théorie des nombres), Années 1989/90-1990/91)

Jerzy Urbanowicz Institute of Mathematics Polish Academy of Sciences

ul. Sniadeckich 8 00-950 Warszawa, Poland

The end of the proof of Lemma 6 should be corrected. Lines from 13 to the end of page 17 should read:

"Thus in view of

ç , ç _ / * o ( < * / 4 ) , if 4 II d,

1 + 4 \ 2t0(d/4, a = ± 3 (mod 8)) if 8 | d,

and

( ) s s _ ( -toW), if 4 || d,

[ J °2 + °3 ~ \ -2t0(d/4, a = ± 1 (mod 8)), if 8 | d,

we obtain

(**) t0(S, a = ± 3 (mod 8)) = 0.

Therefore (3.27) implies

tk = \ t 2 (mod 2o r d 2 k + 6) , and by Lemma 2, the lemma follows." •

As for détails, (*) follows from

d \ ( d \ f d\

(5/2 + ay \ê/2 — a J \a J

(which holds for 0 < a < 6/4: in ail the cases), and (**) is a conséquence of

t0(d/4,a = ±3 (mod 8)) = t0(d/4, a = ± 1 (mod 8)) = t0(d/8, a = -6* (mod 4)) (which holds for d = ±8d*).

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