Problems & Puzzles:
Problems
Problem 11.- Here you are asked to find
primes of the following form
(pr - 1)/(pd
-1), expressible in more than one way.
- Batman asks if 31=(25
- 1)/(2 -1)=(53 -1)/(5-1) is the only
primes which is expressible in more than one way
in the form (pr - 1)/(pd
-1) where p is prime also, r=>3, and d=>1.
No other has been found below 1010.
- If the condition that p be
prime is relaxed the problem goes to Goormaghtigh
and we have the only known solution :
8191=(213-1)/(21)=(9031)/(90-1).
In both cases : can you find
other examples?
(Ref. 2, p. 81, B25)
(See also Puzzle 61)
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