A1:
24 |^ 2 = 24 * 24
by WSIERP_1:1;
A2:
49 |^ 4 = ((49 * 49) * 49) * 49
by POLYEQ_5:3;
17 + 7,7 are_congruent_mod 17
;
then
24 * 24,7 * 7 are_congruent_mod 17
by INT_1:18;
then
(24 |^ 2) |^ 4,49 |^ 4 are_congruent_mod 17
by A1, GR_CY_3:34;
then A3:
((24 |^ 2) |^ 4) + 1,(49 |^ 4) + 1 are_congruent_mod 17
;
17 * 339106, 0 are_congruent_mod 17
;
then
((24 |^ 2) |^ 4) + 1, 0 are_congruent_mod 17
by A3, A2, INT_1:15;
hence
17 divides (24 |^ (2 |^ 3)) + 1
by Lm3, NEWTON:9; verum