No
9
- Let's multiply the first four positive
integers together: 1x2x3x4 = 24.
- Obviously 5 does not divide 24 but it
does divide 1 more than 24.
- Now let's try the first five positive
integers multiplied together: 1x2x3x4x5 = 120.
- This time 6 does divide 120 and does
not divide 1 more than 120.
- The next case is: 1x2x3x4x5x6 = 720.
Does 7 divide this? Does 7 divide 1 more than 720?
|
n
|
1x2x...x(n-1)
|
- divides by
- n?
|
1x2x...x(n-1) + 1
|
- divides by
- n?
|
|
2
|
1
|
no
|
1+ 1
|
yes
|
|
3
|
1x2
|
no
|
1x2 + 1
|
yes
|
|
4
|
1x2x3
|
no
|
1x2x3 + 1
|
no
|
|
5
|
1x2x3x4
|
no
|
1x2x3x4 + 1
|
yes
|
|
6
|
1x2x3x4x5
|
yes
|
1x2x3x4x5 + 1
|
no
|
|
7
|
1x2x3x4x5x6
|
no
|
1x2x3x4x5x6 + 1
|
yes
|
Continue this table and observe something
amazing about the pattern of yes/no answers in the last
column.
- What has this to do with a man called
Wilson?
-
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