Why is Eight Six(es) Afraid of a Single Seven? Because There's No Nine in this joke!
Number Theory
Level
2
What is the remainder when the following number is divided by ?
1
3
46
2
9
36
5
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1 solution
6 6 6 . . . . is a perfect sixth power. a 6 − 1 = ( a 3 − 1 ) ( a 3 + 1 ) = ( a − 1 ) ( a 2 + a + 1 ) ( a + 1 ) ( a 2 − a + 1 ) . In this case, we see that 6 6 6 . . . . − 1 can be factorised to give a factor of 6 + 1 = 7 .