2023 IOQM/Problem 11
Problem
A positive integer haas the property that
is expressible in the form
, where n is an integer. Find the maximum value of
.
Solution
. Now we try to complete the square, multiplying by
and
won't complete the square but on multiplication with
we get
or
.
:
and
and
,
.
:
and
and
,
.
:
and
and
,
.
:
and
and
,
.
Thus the maximum value of .
~Lakshya Pamecha and Parveen Sir