khulna math club probs
Posted: Wed Jan 26, 2011 9:41 pm
1.9 points are inscribed in a square with side length 1.prove that that is at least 3 points which make a triangle with area less than $$\frac{1}{8}$$
2what is the largest factor of $$11!$$ which has remainder 1 if divided by 6?
3.if $$mn$$ divides $$m^2+n^2+m$$,prove that $$m$$ is a square number.(m and n are integers)
4.$$a_1,a_2,... $$ is a sequence of non-negative real numbers
for all n $$a_n+a_{2n} \geq 3n$$ and $$a_{n+1}+n \leq 2 \sqrt{a_n(n+1)}$$
prove that for all n $$a_n \geq n$$
[took my sweat out to post the last prob so at least read it 1ce
]
2what is the largest factor of $$11!$$ which has remainder 1 if divided by 6?
3.if $$mn$$ divides $$m^2+n^2+m$$,prove that $$m$$ is a square number.(m and n are integers)
4.$$a_1,a_2,... $$ is a sequence of non-negative real numbers
for all n $$a_n+a_{2n} \geq 3n$$ and $$a_{n+1}+n \leq 2 \sqrt{a_n(n+1)}$$
prove that for all n $$a_n \geq n$$
[took my sweat out to post the last prob so at least read it 1ce
]