Difference between revisions of "2023 IOQM/Problem 11"
(Created page with "==Problem== A positive integer <math>m</math> haas the property that <math>m^2</math> is expressible in the form <math>4n^2-5n+16</math>, where n is an integer. Find the maxim...") |
(No difference)
|
Revision as of 12:18, 2 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 , .
Thus the maximum value of .
~Lakshya Pamecha and Parveen Sir