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Area Man Who Talks a Lot About Teaching Teaches His First Full Day in >10
Years
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I have taught demo and observational classes regularly since I left
full-time teaching but yesterday was the first time I taught every class
for the day. L...
2 years ago
The answer is 161.
ReplyDelete1/x + 1/y = 1/210
(x+y)/(xy) = 1/210
xy = 210(x+y)
xy - 210x - 210y = 0
(x - 210)(y - 210) = 210^2
Now, 210^2 has 81 positive divisors and 81 negative divisors. So there are 162 possible values for x - 210, and y - 210 is determined by x - 210. However, we must exclude the case where x - 210 = y - 210 = 210, because this leads to division by zero.
Therefore the number of integer solutions is 2*81-1 = 161.