Remaining remainder!
Number Theory
Level
2
Find the remainder when is divided by 20.
19
12
15
17
10
13
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1 solution
Starting with 5 ! if we expand the factorials at some point we find . . . 4 × 5 . . . meaning all of those are 0 in modulo 2 0 . Now just find the first 4 terms mod 20: 1 ! + 2 ! + 3 ! + 4 ! = 3 3 ≡ 1 3 ( m o d 2 0 )