Find the triplet (a,b,c) of positive integers satisfying this equation:
a3 + b4 = c5
such that a+b+c is the minimum.
In retrospect, after finding by computer, the solution is:
(2^8)^3 + (2^6)^4 = (2^5)^5
(a,b,c) = (256, 64, 32)
whose sum is 352
-----------
amax = 1000
bmax = amax
cmax = int((amax**3 + bmax**4)**.2)
a_s = [n**3 for n in range(1,amax+1)]
b_s = [n**4 for n in range(1,bmax+1)]
c_s = [n**5 for n in range(1,cmax+1)]
for a in a_s:
for b in b_s:
if a + b in c_s:
print(a,b, a + b,(a + b )**.2)
print(round(a**(1/3)), round(b**(1/4)), round((a+b)**.2))
print(sum([round(a**(1/3)),
round(b**(1/4)),
round((a+b)**.2)]))
|
|
Posted by Larry
on 2024-12-03 09:03:10 |
Computer solution