Prove that for all naturals $n \ge 6$ there is a set of $n$ positive naturals, $a_1$ to $a_n$ such that $\sum_{i=1}^n \left(\frac{1}{a_i}\right)^2 =1$

score 59 · Answer 6 · 2015-04-14 18:57:15

If $0 < \frac{a}{b} < 1$, does subtracting the next largest number $\frac{1}{n}$ always make the resulting fraction's numerator less than $a$?

score 48 · Answer 7 · 2015-06-04 03:57:17

48

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score 926 · Answer 8 · 2015-08-03 06:30:53

926

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score 151 · Answer 9 · 2016-04-05 01:02:51

151

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score 493 · Answer 10 · 2016-04-11 14:12:08

493

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Find all integer solutions to $\frac{1}{x} + \frac{1}{y} = \frac{2}{3}$

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score 3.9k · Answer 11 · 2013-08-02 19:42:02

3.9k

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score 296 · Answer 12 · 2013-08-17 19:27:18

296

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score 386 · Answer 13 · 2013-08-31 01:38:46

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score 789 · Answer 14 · 2013-10-07 14:19:36

789

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score 633 · Answer 15 · 2013-10-20 18:14:31

633

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Prove that for all naturals $n \ge 6$ there is a set of $n$ positive naturals, $a_1$ to $a_n$ such that $\sum_{i=1}^n \left(\frac{1}{a_i}\right)^2 =1$

If $0 < \frac{a}{b} < 1$, does subtracting the next largest number $\frac{1}{n}$ always make the resulting fraction's numerator less than $a$?

Under what conditions would the function $\prod_{i=1}^{n}{\frac{r_i}{r_i - 1}}$ be decreasing with respect to $n$?

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