1. Quote of the month: "Friendship is like money - easier made than kept" - Samuel Butler
2. New quiz AQQ300 about a divisibility by 6 puzzle
Good luck and try to be among the first ones!
1. Quote of the month: "Friendship is like money - easier made than kept" - Samuel Butler
2. New quiz AQQ300 about a divisibility by 6 puzzle
Good luck and try to be among the first ones!
Factor (n5-n) into n(n-1)(n+1)(n2+1) then divide by 2x3.
Equation A:
For some odd numbers, n/3 is an integer. If the remainder of n/3 is 1/3, then (n-1)/3 is an integer. If it is 2/3, then (n+1)/3 is an integer. The second term is an integer since (n2+1) is an even number.
Equation B:
For the first term, n/2 is an even integer. For the second term, If the remainder of n/3 is 1/3, then (n-1)/3 is an integer. If it is 2/3, then (n+1)/3 is an integer
Equation C:
For the first term, n/6 is an integer.
This covers the range of n >= 0 and shows that whatever n is, the result of (n5-n)/6 is an integer (i.e. it’s divisible by 6).
Factor (n5-n) into n(n-1)(n+1)(n2+1) then divide by 2x3.
Equation A:
For some odd numbers, n/3 is an integer. If the remainder of n/3 is 1/3, then (n-1)/3 is an integer. If it is 2/3, then (n+1)/3 is an integer. The second term is an integer since (n2+1) is an even number.
Equation B:
For the first term, n/2 is an even integer. For the second term, If the remainder of n/3 is 1/3, then (n-1)/3 is an integer. If it is 2/3, then (n+1)/3 is an integer
Equation C:
For the first term, n/6 is an integer.
This covers the range of n >= 0 and shows that whatever n is, the result of (n5-n)/6 is an integer (i.e. it’s divisible by 6).
