But That Number Is Huge!
True or false :
1 1 1 1 1 1 7 is divisible by 6.
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3 solutions
I did it the same way, but instead of calculating 7 6 , write it as ( 1 + 6 ) 7 , and then using binomial expansion we get our answer
1 1 1 1 1 1 7 ≡ ≡ ≡ 7 5 + 7 4 + 7 3 + 7 2 + 7 1 + 7 0 1 + 1 + 1 + 1 + 1 + 1 0 ( m o d 6 )
Exactly how I did it!
This is an analogy of divisibility rule of
9
in base
1
0
.
The divisibility rule of
6
in base
7
is the same: sum them up:
1
+
1
+
1
+
1
+
1
+
1
=
6
which is clearly divisible by
6
.
Answer is True.
1 1 1 1 1 1 7 1 9 6 0 8 = ( 7 5 + 7 4 + 7 3 + 7 2 + 7 1 + 7 0 ) 1 0 = 7 − 1 7 6 − 1 = 1 9 6 0 8 ≡ 0 ( m o d 6 )