Difference between revisions of "2023 IOQM/Problem 11"
(→Solution) |
(→Solution) |
||
Line 10: | Line 10: | ||
Thus the maximum value of <math>|m-n|=\boxed{14}</math>. | Thus the maximum value of <math>|m-n|=\boxed{14}</math>. | ||
− | ~Lakshya Pamecha | + | ~Lakshya Pamecha (Inspired by Parveen Sir) |
Revision as of 02:59, 4 May 2024
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
,
.
Other cases in which the value of and
interchange, the values of m and n will not change in those cases.
Thus the maximum value of
.
~Lakshya Pamecha (Inspired by Parveen Sir)