Question

Find the remainder when dividing 8! -1 by 11
( use congruent congruence)

Answer 1

Congruence

We can solve it easier, if we multiply two numbers at once.

$8!=(8\times7)\times...\times(2\times1)$

56≡1(mod 11)

30≡8(mod 11)

12≡1(mod 11)

2≡2(mod 11)

Now, we can observe that

8!≡16≡5(mod 11)

And now,

8!-1≡4(mod 11)