Few problems - 4
![Few problems - 4](/content/images/size/w2000/wordpress/2017/06/banner_problemsolving.gif)
- Find all integers
satisfying
such that
is a divisor of
.
- Find the number of ordered pairs
of positive integers which satisfy
.
- The integer
consists of 2017 consecutive nines. A computer calculates
. How many nines does the number
contain in total ?
- 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
.
- Let
where
is an integer. Prove that
cannot be expressed as the product of two non-constant polynomials with integer coefficients.