Waste less time on Facebook — follow Brilliant.
×

Some questions of UKMO

(\(1\)) If \(a,b\) and \(c\) are real numbers such that \(a<b<c\), \(a+b+c=6\) and \(ab+bc+ca=9\).

Prove that \(0<a<1<b<3<c<4\).


(\(2\)) Find all triples (\(a,b,c\)) such that

\[\left(1+\frac{1}{a}\right)\left(1+\frac{1}{b}\right)\left(1+\frac{1}{c}\right)=2\]


(\(3\)) How many perfect squares are there \(\pmod{ 2^n}\)?


Please post your solutions!

Note by Akshay Yadav
6 months, 1 week ago

No vote yet
1 vote

Comments

There are no comments in this discussion.

×

Problem Loading...

Note Loading...

Set Loading...