Bhaskara Contest 2013 Level-II

Find all ordered values integers $x,y,z$ such that $xy+yz+zx=xyz+2$ Please post the solutions too!

#NumberTheory #OrderedPairs #IntegerRoots

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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}`	$2^{34}$
`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}`	$\boxed{123}$

Comments

Wait, Is Bhaskara contest held in Delhi too? W.R.T Solutions- sorry, I dont think I have solved it fully but what came to my mind as soon as i saw this is - factor. Like if you see $(x+1)(y+1)(z+1)$ you will get most of the terms which are there in the question. Ill work on it and tell you. Are you taking up the test tomo'w? Well- A small change- The signs must be reversed with the 1's!

Krishna Ar - 6 years, 9 months ago

Yes, it takes place in Delhi too. However, in not held on such a vast scale as in TN. According to me a better form of factorization is $(x-1)(y-1)(z-1)$ . And I am giving NMTC today.

Siddharth G - 6 years, 9 months ago

Yes. Sorry that I messed up the signs! I did want to change it but I fell asleep as I was on the bed while typing :P. Post your score too on the discussion I (plan to) start today after NMTC on Brilliant!

Krishna Ar - 6 years, 9 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}`	$\boxed{123}$