Consider this Diophantine equation:
3
a + 4
b + 5
c = 6
d, where each of a, b, c, and d is a positive integer.
The famous ancient Greek philosopher and mathematician Plato
was aware that a=b=c=d=3 is a solution.
Does there exist any further solution?
Authenticate your answer with valid arguments.
I only found one other solution in addition to the one previously known.
(a,b,c,d) = (3,1,1,2)
3^3 + 4^1 + 5^1 = 6^2
27 + 4 + 5 = 36
-------
import math
big = 100
for a in range(1,big+1):
for b in range(1,big+1):
for c in range(1,big+1):
x = 3**a + 4**b + 5**c
log6 = int(math.log(x,6))
for d in range(log6,log6+2):
if x == 6**d:
print(a,b,c,d)
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Posted by Larry
on 2022-06-09 06:58:24 |
computer Solution without formal proof
