Question

Determine the maximum value

Answer 1

limit
limit, maximum, threshold, constraint, cutoff point, check, ceiling, cap

Answer 2

of \[m^2+n^2\],where m and n are intergers satisfying \[m,n \in\left\{1,2,3...1981 \right\}\]and
\[(n^2-mn-n^2)^2=1\]

Answer 3

last one is supposed to be\[(n^2-mn-m^2)^2=1\]

Answer 4

Are you sure you don't have to write a program for this?

Answer 5

no its says no calculator

Answer 6

NO calculator either. Wow, good luck playing with the combinations bro.

Answer 7

thanksi really need it

Answer 8

I'd be happy if I found an (n,m) combination that equaled 1. When you tack on finding the max value, that increases the difficulty even more. It wasn't enough to try to find (n,m) = 1. They had to get you to find the max value as well.

Answer 9

the question was likely asked in 1981

Answer 10

well let mesay whatyou can findcan help lot like finding ,max (n,m)

Answer 11

Calculators existed in 1981 bro

Answer 12

Even if you found max(n,m) the combination would still have to equal one

Answer 13

lol,and we had good mathematicieans before1800 before wolfram

Answer 14

Yeah, finding possible max values would be a good first strategy.

Answer 15

Yes, but it took them months to solve problems that it takes seconds to solve now.

Answer 16

They were good....for their time.

Answer 17

can i use calculus to optimise m^2+n^2

Answer 18

Yes, of course.

Answer 19

does that help

Answer 20

\[((n+m)^2-3mn)^2=1\]

Answer 21

I don't even know how you got that. I thought you were going to find derivative of m^2 + n^2

Answer 22

man this thing is heavy for me i am just trying sme random ideas

Answer 23

look at this http://www.artofproblemsolving.com/Wiki/index.php/1981_IMO_Problems/Problem_3

Answer 24

Bro, you were on the right track with finding the derivative of m^2 + n^2

Answer 25

did you see the link

Answer 26

seems to be Fibonacci

Answer 27

http://www.artofproblemsolving.com/Wiki/index.php/1981_IMO_Problems/Problem_3

Answer 28

@Hero see this