Lets Solve A Nice Diophantine Equation

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Комментарии
Автор

As sqr(20) = 2·sqr(5) and we are loking for integer solutions, sqr(x) and sqr(y) must be written as k·sqr(5) in order to cancel the irrational part. So,

1/k + 1/m = 1/2 (k, m positive integers)

And the only possibilities are (1/3 + 1/6) and (1/4 + 1/4) because if k i greater or equal to 5 (1/k <= 0.2) there is no m which verify 1/m >= 0.8.

FisicTrapella
Автор

Enjoyed this one. I got one pair pretty quickly since I knew that 1/2 + 1/2 = 1 so 1/sqrt(x) and 1/sqrt(y) both could be half of 1/sqrt(20), and that's an easy thing to solve But that's not going to help anyone find the other possibilities.

Qermaq