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.


 
1 CLS
2 DIM k(29): DIM q(249)
5 FOR i=4 TO 249: LET q(i)=LN i : NEXT i
6 REM enhancements for the much expanded Spectrum Next:  DIM p(248,249)
7 REM FOR j=4TO 248:FOR i=j TO 249:LET p(j,i)=EXP (q(j)-q(i))*5:NEXT i:NEXT j
9 PRINT "slide rule ready"
15 FOR i=0 TO 9: LET k(i)=240+ i : NEXT i
17 FOR i=10 TO 29: LET k(i)=210+ i : NEXT i
20 FOR w=6 TO 246 STEP 3
21 LET o=w
22 FOR x=4 TO 248 STEP 2
23 IF o<x THEN LET o=x
24 FOR y=10 TO 245 STEP 5
25 IF o<y THEN LET o=y
26 FOR z=14 TO 245 STEP 7
27 IF o<z THEN LET o=z
30 LET o=o+1 : LET m=k(FN f((w+x+y+z),30))
34 IF m<o THEN GO TO 90
40 REM LET s=p(w,m)+p(x,m)+p(y,m)+p(z,m) instead of:
42 LET s=EXP((q(w)-q(m))*5)
43 LET s=EXP((q(x)-q(m))*5)+ s
45 LET s=EXP((q(y)-q(m))*5)+ s
47 LET s=EXP((q(z)-q(m))*5)+ s
50 IF s<>1 THEN GO TO 80
52 LET a=FN f(w*w,m) : LET a=FN f(a*a*w,m)
53 LET b=FN f(x*x,m) : LET b=FN f(b*b*x,m)
55 LET c=FN f(y*y,m) : LET c=FN f(c*c*y,m)
57 LET d=FN f(z*z,m) : LET d=FN f(d*d*z,m)
60 LET u=FN f((a+b+c+d),m)
65 IF u THEN GO TO 80
73 PRINT w;"^5+";x;"^5+";y;"^5+";z;"^5=";m;"^5": STOP
80 IF s<1 THEN m=m-30 : GO TO 34
90 NEXT z: NEXT y: NEXT x: NEXT w
100 DEF FN f(e,n)=e- INT(e/n)*n
 