MathLabs

Problem 3

Determine the maximum value of m2+n2m^2+n^2, where mm and nn are integers satisfying m,n∈{1,2,…,1981}m, n \in \{1, 2, \ldots, 1981\} and (n2−mn−m2)2=1(n^2-mn-m^2)^2 = 1.
Step 6 of 6: Compute the maximum value
Previous stepNext step
9872+15972=974169+2550409=3524578987^2+1597^2 = 974169+2550409 = 3524578
Detailed analysis

Since m2+n2m^2+n^2 increases along the Fibonacci chain, the maximum over all admissible pairs is achieved at the largest one found in Step 5, giving 9872+15972=3524578987^2+1597^2=3524578.