Can you solve the following equation?
½ = 1/x² + 1/y² +...+ 1/z²
All variables must be different, positive integers, and there must be a finite number of terms.
A computer program comes up with the following variables:
2,3,4,5,6,11,54,519,59429
which totals about 0.4999999999999980848
and has some indication that starting an infinite series at 22686937 would help complete the total.
The program follows, and actually assumes that 2 will be one of the variables and starts from there without reporting the 2.
DECLARE SUB try (n#)
CLEAR , , 4000
DEFDBL AZ
DIM SHARED lim, tot, used, remain, trm(50), howMany
pi = ATN(1) * 4
lim = pi * pi / 6  1.25
tot = 0
used = 0
remain = lim
try 3
SUB try (n)
term = 1 / (n * n)
rSave = remain
remain = remain  term
IF ABS(term + used  .25) < 1E12 THEN
FOR i = 1 TO howMany
PRINT trm(i)
NEXT
PRINT n
END IF
IF term + used <= .25 + 1E12 THEN
uSave = used
used = used + term
howMany = howMany + 1
trm(howMany) = n
try n + 1
howMany = howMany  1
used = uSave
END IF
IF remain >= .25  used THEN
rSave = remain
uSave = used
need = 1 / SQR(.25  used)
new = INT(need)
FOR i = n + 1 TO new  1
term = 1 / (i * i)
remain = remain  term
NEXT i
try new
used = uSave
remain = rSave
END IF
remain = rSave
END SUB
with output
3
4
5
6
11
54
519
59429
22686937
22686938
22686939
22686940
22686941
22686942
22686943
22686944
22686945
22686946
22686947
22686948
22686949
22686950
22686951
22686952
22686953
22686954
22686955
22686956
22686957
22686958
22686959
22686960
22686961
22686962
22686963

Posted by Charlie
on 20040921 10:29:01 