- Let be an acute angled triangle such that . Let be a point on such that . Let be an internal point of the segment . Prove that if and only if .
- Show that there are infinitely many positive integers such that .
- Show that is always composite for all natural numbers . (Hint : Factorise )
- Show that the number of natural numbers divisible by less than or equal to is .
- For real numbers prove that
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