There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin.



Euler's (disproved) sum of powers   conjecture

  At least  k  positive  kth  powers are required to sum to a  kth  power,  
  except for the trivial case of one  kth power:  yk = yk 



In 1966,   Leon J. Lander   and   Thomas R. Parkin   used a brute-force search on a   CDC 6600   computer restricting numbers to those less than 250.



Task

Write a program to search for an integer solution for:


  x05 + x15 + x25 + x35 == y5 

Where all     xi's   and    y    are distinct integers between   0   and   250   (exclusive).

Show an answer here.



Related tasks

   Pythagorean quadruples. 
   Pythagorean triples.


MAX=250
pow5=()
for (( i=1; i<MAX; ++i )); do
  pow5[i]=$(( i*i*i*i*i ))
done
for (( a=1; a<MAX; ++a )); do
  for (( b=a+1; b<MAX; ++b )); do
    for (( c=b+1; c<MAX; ++c )); do
      for (( d=c+1; d<MAX; ++d )); do
        (( sum=pow5[a]+pow5[b]+pow5[c]+pow5[d] ))
        (( low=d+3 ))
        (( high=MAX ))
        while (( low <= high )); do
          (( guess=(low+high)/2 ))
          if (( pow5[guess]  == sum )); then
            printf 'Found example: %d⁵+%d⁵+%d⁵+%d⁵=%d⁵\n' "$a" "$b" "$c" "$d" "$guess"
            exit 0
          elif (( pow5[guess] < sum )); then
            (( low=guess+1 ))
          else
            (( high=guess-1 ))
          fi
        done
      done
    done
  done
done
printf 'No examples found.\n'
exit 1