Question 279896: The people at a meeting of Goodtime Sports are forming equal teams. When they form groups of 2, 3, 4, 5, or 6 there is always exactly one person left. What is the smallest number of people that could be at the meeting?
Answer by Edwin McCravy(20065)   (Show Source):
You can put this solution on YOUR website! The people at a meeting of Goodtime Sports are forming equal teams. When they form groups of 2, 3, 4, 5, or 6 there is always exactly one person left. What is the smallest number of people that could be at the meeting?
One more than any multiple of p, say qp, will
leave a remainder of 1 when divided by p.
Proof:
q
-------
p)qp + 1
qp
--
1
Conversely, if a remainder of 1 is left when integer
n is divided by p, then n is one more than a mutiple of p.
Proof:
Suppose
q
-----
p) n
pq
--
1
Then qp+1 = n
Therefore 1 more than the least common multiple of 2, 3, 4, 5, and 6
will be the least positive integer that will leave a remainder of 1
when any of these are divided into it.
The least common multiple of 2,3,4,5, and 6 is 60, so one more than that,
61, is the desired integer.
Edwin
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