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# Nice problem!

Find all integer solution to $$\frac{2}{a^{2}}+\frac{3}{b^{2}}+\frac{4}{c^{2}}=1$$. Just give me a correct hint or the approach with which I must start it.Please dont give me the solution.

Note by Kishan K
4 years, 1 month ago

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There's a general trick here: attempt to bound one of the terms.

Let m = min(a, b, c), then $$a \ge m \implies \frac 1 {a^2} \le \frac 1 {m^2}$$. Then:

$1 = \frac 2 {a^2} + \frac 3 {b^2} + \frac 4 {c^2} \le 4\left( \frac 1 {a^2} + \frac 1 {b^2} + \frac 1 {c^2}\right) \le \frac {12}{m^2}$

So $$m^2 \le 12$$ and m = 2, 3. Consider each of a=2,3; b=2, 3 and c=3. · 4 years, 1 month ago

Go to http://www.amtionline.com/ · 4 years, 1 month ago

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is it possible with just one equation? · 4 years ago

subhrodiptob@yahoo.com! i am amazed my your mathematics excellence at age of only 13!!! · 4 years, 1 month ago

cool prob which book u get this from?- mooremichael493@gmail · 4 years, 1 month ago

Kevin, can i get your book in pdf or in word to 'playing' with your exc? my email is umaraburrohman.94@gmail.com · 4 years, 1 month ago

What's the source of this problem? · 4 years, 1 month ago

My book. · 4 years, 1 month ago

what's the name of the book? · 4 years, 1 month ago

Which one is it? Does it contain more problems like this? · 4 years, 1 month ago

Yes many. · 4 years, 1 month ago

i am interested also.... heres my email mharfemicaroz@gmail.com

please send to me.. i have very poor math skills:( · 4 years ago

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Kevin, I want too, my email: leonardochandra@hotmail.com. Thanks · 4 years, 1 month ago