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henpen
 3 years ago
How many integer n exist so that \[ \frac{n}{100n} \] is also an integer?
henpen
 3 years ago
How many integer n exist so that \[ \frac{n}{100n} \] is also an integer?

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henpen
 3 years ago
Best ResponseYou've already chosen the best response.0What is the general strategy to be adopted for 'How many integer n exist so that f(n) is also an integer?', other than bursts of insight?

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0i think, trial error is the best way for this case

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.3suppose that for some integer k, \[k=\frac{ n }{ 100n }\] rearranging the equation we get \[n=\frac{ 100k }{ k+1 }\] and since k and k+1 are relatively prime, we conclude that \[(k+1)100\]

henpen
 3 years ago
Best ResponseYou've already chosen the best response.0What does the notation (k+1)100 mean?

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.3when k = 0, n = 0. when k = 1, n = 50 when k = 3, n = 75

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.3there are more values for k, but the solution set is finite.
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