perplexus.info :: Numbers : A little Generalization

A little Generalization (Posted on 2012-12-18)

Observe that
1/1+1/3=4/3;4^2+3^2=5^2
1/3+1/5=8/15;8^2+15^2=17^2
1/5+1/7=12/35;12^2+35^2=37^2
State and prove the generalization suggested by the above examples.

No Solution Yet Submitted by Danish Ahmed Khan

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Two consecutive odd/even unit fractions

Comment 2 of 2 |

It works also when we take two consecutive even numbers.

1/(2*k) + 1/(2*k+2) = (2*k+1)/(2*k(k+1))

(2*k + 1)^2 + (2*k(k + 1))^2 = (2*k(k+1) + 1)^2

However, this method does not generate all the primitive Pythagorean triangles.

Reference:

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html#towunitractsodd

Posted by Benny on 2012-12-21 16:45:45

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