Few Problems - 3

- 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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