let n be Nat; ( n <= 1105 & n is composite & n divides (2 |^ n) - 2 & n divides (3 |^ n) - 3 implies n in {561,1105} )
assume
( n <= 1105 & n is composite & n divides (2 |^ n) - 2 )
; ( not n divides (3 |^ n) - 3 or n in {561,1105} )
then
n in {341,561,645,1105}
by Th49;
then
( n = 341 or n = 561 or n = 645 or n = 1105 )
by ENUMSET1:def 2;
hence
( not n divides (3 |^ n) - 3 or n in {561,1105} )
by Th50, Th56, TARSKI:def 2; verum