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.

#NumberTheory #MathProblem #Math

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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.

C Lim - 7 years, 11 months ago

Go to http://www.amtionline.com/

Kishan k - 7 years, 11 months ago

This book is not very good it is not for exam of higher level than your local exams conducted my private companies.Questions on brilliant are far far better than this.So don't bother about it anymore.Yes, If u really want to excel in mathematics get Problem Solving Strategies.Really, you will enjoy it.

Kishan k - 7 years, 11 months ago

What's the source of this problem?

Tim Vermeulen - 7 years, 11 months ago

My book.

Kishan k - 7 years, 11 months ago

Which one is it? Does it contain more problems like this?

Tim Vermeulen - 7 years, 11 months ago

@Tim Vermeulen – Yes many.

Kishan k - 7 years, 11 months ago

@Kishan K – give it to mee too

advitiyabrijesh@gmail.com

Advitiya Brijesh - 7 years, 11 months ago

@Kishan K – me too ............ anshul99agr@gmail.com

ANSHUL AGARWAL - 7 years, 11 months ago

@Kishan K – may I have one? serlyayus@gmail.com

Serly Zubir - 7 years, 10 months ago

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

please send to me.. i have very poor math skills:(

Mharfe Micaroz - 7 years, 10 months ago

@Tim Vermeulen – Give me ur email, I will send u all information of it.

Kishan k - 7 years, 11 months ago

@Kishan K – Kevin, I want too, my email: leonardochandra@hotmail.com. Thanks

Leonardo Chandra - 7 years, 11 months ago

@Kishan K – chaukhanh1603@yahoo.com.vn

Chau Bui - 7 years, 11 months ago

@Kishan K – here potsunsi@yahoo.com i really interested..

Abdul Mu'min Unsi - 7 years, 10 months ago

@Kishan K – pls send me too.....my mail is kislay4raj@gmail.com

Kislay Raj - 7 years, 10 months ago

what's the name of the book?

Bhargav Das - 7 years, 11 months ago

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

Umar Abdurrohman - 7 years, 11 months ago

cool prob which book u get this from?- mooremichael493@gmail

michael moore - 7 years, 11 months ago

subhrodiptob@yahoo.com! i am amazed my your mathematics excellence at age of only 13!!!

Subhrodipto Basu Choudhury - 7 years, 11 months ago

is it possible with just one equation?

Sudipto Chowdhury - 7 years, 10 months ago

I have posted the name of the website.Many of you would be knowing it, or everyone would be.Don't go for this book it has very few questions, go for Problem Solving Strategies...Best ever book......Try to solve first few problems of it,I am not telling to solve all but few, and try to solve as many as u can....

Kishan k - 7 years, 10 months ago

Listen Kevin. You have got skill, talent and opportunity in front of you. Don't waste it trying to pursue some engineering degree from IIT. Instead, develop your skill and try to advance in a science stream of your choice. This is just my opinion out of my personal experience. No hard feelings against any engineering degree, engineers or any IIT.

Chinmmayya Hajare - 7 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$