Will You Dare To Solve This Equation ? Olympiad Mathematics @mathsmood​

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Автор

1/20 + 1/380 works. Start a little smaller than 1/19 and nudge it up. 20 x 19 = 380.
Here's another one: 1/x + 1/y = 1/21. Start a little smaller and nudge it up: 1/22 + 1/y = 1/21. 22 x 21 = 462. 1/22 + 1/462 = 1/21? Yep.
Let's get a formula going! 😄😄

jim
Автор

Nice work. A few comments. (1) At 0:54 you asserted either x or y must be a multiple of 19 but you did not say why. The reason is that 19 is prime. (2) At 3:30 you said there would be "many" cases. The reason the problem is tractable here is that there aren't "many" cases, rather, there are only a few cases, again, because 19 is prime. (3) This whole solution hinges on the RHS denominator being a prime number. If the RHS denominator had been composite, how would you have solved the problem?

brianwade