Find all integers $a,b,c$ such that $a^2 = bc + 1$ and $b^2 = ac + 1$
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06.12.2015 14:33
got 8 ordered solutions
06.12.2015 14:33
@shashank how many solutions do u get?
06.12.2015 14:34
@pjmaths i got 8 too
06.12.2015 14:35
Our question was slightly different. It was $bc+4$ and $ac+4$ as opposed to $bc+1$ and $ac+1$.
06.12.2015 14:40
shashank123 wrote: Our question was slightly different. It was $bc+4$ and $ac+4$ as opposed to $bc+1$ and $ac+1$. dear Shashank, It would be highly grateful if u post the questions of ur region
06.12.2015 14:44
@Shashank which region r u frm?
06.12.2015 15:09
very easy question for rmo my solution = we easily get $a^3-b^3=a-b$ which gives either $a=b$ or $a^2+b^2+ab=1$ for second case $a^2+b^2+ab=1$ we easily get that $c=-(a+b)$ and hence $a^2+b^2+c^2=2$ this kills the question.
10.12.2015 17:06
All, I am from Karnataka. I believe the questions have been posted already.