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Great Granddad
By Charlie Gilderdale on Friday, May 10, 2002 - 03:32 pm:

Great Granddad was one of The March Six Problems.
See http://www.nrich.maths.org/mathsf/journalf/mar02/stage3new.html

We published a solution from Andrei Lazanu that attempted to show that there was a unique solution.
See http://www.nrich.maths.org/mathsf/journalf/mar02/stage3_s.html

We have since had an email from Julia Collins, saying:
"I have read Andrei's solution to this problem and don't believe that he has shown it to be a unique solution.
Firstly, the question did not put a limit on when the man was born - it could be in the future, in which case x does not have to be smaller than 32.
Secondly, B does not have to be of the form 2×x2 because if x is even then the prime does not have to be 2. Is there another solution that does not involve simply checking that no other solution is possible?

Best wishes,
Julia Collins"

I thought I would publish Julia's message here so that everybody can contribute to the follow-up discussion.

Charlie Gilderdale
NRICH Project

By Kondwani Kanjere on Friday, May 10, 2002 - 06:14 pm:

Is it true that only the squares of even numbers are even? If it is true then that limits the values x can take (i.e only even number) on the condition that the prime is not 2 but some other primes.
This might give a guide in proving the uniqueness of Andrei's solution.
I havent come up with a proof YET which doesnt involve checking that no other solution is possible, but I believe this is another valuable approach in proving the uniqueness of the solution.

By Andrei Lazanu on Wednesday, May 15, 2002 - 05:40 am:

This is a reply to Julia's message, regarding my solution to Great Granddad.

1) You are right, the other possibility:

A -> 2 * prime
A + 20 -> prime * 22
A + 80 -> 2 * prime
A + 100 -> 2 * prime * prime * prime

must be taken into account, but it does not give more solutions:

As A + 20 (it means B) is divisible by 4, A is also; C and D are they too divisible by 4. So, A must be 4 and C must be 4. This isn't possible, because C – A = 80.

2) I worked up to D = 2002, while I thought that "Great Granddad" could be a real person. For the future, may be there are other solutions to the problem.