Determine all triplet(s) (p, q, r) of positive integers that satisfy the equation:
(5)p * (43)q + 1 = r3
I also found only one solution: (p,q,r) = (1,1,6) which I suspect is the only solution, but it would be nice to have an analytical proof of that.
Due to the 5^p term, the LHS is always 6 mod 10, so r^3 must be also.
Therefore the last digit of r can only be 6.
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big = 200
for p in range(1,big):
for q in range(1,big):
for r in range(6,big,10):
if (5)**p * (43)**q + 1 == r**3:
print(p,q,r)
Output: 1 1 6
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Posted by Larry
on 2023-04-01 11:40:26 |
Computer solution
