I also started with bounding x, but then instead of factorization I used bounding for y, which leads to few possible values of y; z can be calculated then.
I guess this wouldn't be on a modern IMO Longlist, as there are so many problems of this kind nowadays, so everyone knows how to solve them. I think yet alone on this channel there are 2 or 3 problems of this kind.
y and z are natural numbers. For that product to be positive, both y and z would have to be less than or equal to 3. But then the sum of 1/x + 1/y + 1/z would be greater than 1.
I also started with bounding x, but then instead of factorization I used bounding for y, which leads to few possible values of y; z can be calculated then.
Same
I guess this wouldn't be on a modern IMO Longlist, as there are so many problems of this kind nowadays, so everyone knows how to solve them. I think yet alone on this channel there are 2 or 3 problems of this kind.
A really good warm up question!
I think it would have been good if you also specified why you skipped negative values for 3y-10 when x=2.
there is no need to specify iy since x,y,z are natural numbers. It is not hard to see that.
y and z are natural numbers. For that product to be positive, both y and z would have to be less than or equal to 3. But then the sum of 1/x + 1/y + 1/z would be greater than 1.
beautifully executed!
I used Egyptian fractions and solved it in under a min 😀
But how does Egyptian fraction give you all solution/prove they are only solutions? does it not just give you a solution
0:03
Lovely
Are there more good ways ( that can help me in my Olympiad) to solve this? If so can someone tell me.
Namaste🙏.
Yes. I solved it.