Hello

Aldrich Stevens noted offline that my result is not correct:

> There must be an error in your program.

> All of your proposed counterexamples

> actually do have values of k that

> satisfy the conditions of the test.

> x = 4, k = 162

> x = 5, k = 247

> x = 6, k = 351, 358

> x = 9, k = 769

and Peter Kosinar again offline located the my mistake:

>> (issquare test: 0 < 5*(2*k-1)^2 - 4*A^2 = f^2)

>> y := 5*(2^k-1)^2 - 4*A^2;

> It seems your code uses 2^k, while the original poster used 2*k.

Thank you Aldrich and Peter

Changing the code as Peter noted

and adding a single dot after 5 in sqrt(5) to avoid maple's symbolic

manipulations

and extending the for x to higher values

the output reads as follows:

4 160-176 (162)

5 245-270 (247)

6 348-384 (351)

9 764-864 (769)

10 938-1040 (952)

...

100 89889-100400 (89893)

...

1000 8948743-10004000 (8959147)

...

Yes, not the conjecture nor its inverse is trivial!

Regards,

Payam

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