p^a+q^b=r^c
How many distinct solutions of the equation above are there, subject to the following constraints:
p, q, & r distinct primes
a, b, & c distinct positive integers,
each
more than one
None of the powers exceeds 1111.
pr=sym(primes(100));
for w1=1:length(pr)
p=pr(w1);
for w2=w1+1:length(pr)
q=pr(w2);
for a=2:11
for b=2:11
if a~=b
rhs=p^a+q^b;
f1=factor(rhs);
f=unique(f1);
if length(f)==1 && length(f1)>1
disp([p a q b f length(f1)])
end
end
end
end
end
end
finds
[2, 4, 3, 2, 5, 2]
[2, 5, 7, 2, 3, 4]
[2, 7, 17, 3, 71, 2]
[7, 3, 13, 2, 2, 9]
before being cut off manually
meaning
2^4 +3^2=5^2 b and c not distinct here -- ignore
2^5 +7^2=3^4
2^7+17^3=71^2
7^3+13^2=2^9
|
|
Posted by Charlie
on 2023-09-23 20:05:21 |
my computer findings
