# A Holiday Brain Teaser

by A. D. Denton

From The Sunday Times, 4th August 1957 [link]

The series below is peculiar in that if any two of the numbers are multiplied together and added to unity, the result is a perfect square:

1, 3, 8

Let A[4], be a fourth number in this series. There is a further series with the same characteristic:

8, B[2], 190, B[4]

in which not only is B[1], the same as A[3], but B[2] is also the same as A[4].

What is B[4]?

(Note: zero is excluded)

3 Comments
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This is an interesting little Brain Teaser that can be solved using the quadratic diophantine solver in my number theory library.

@Brian, could you explain limit values 10 and 12?

@Frits, they are nothing special, just chosen as sufficient to obtain enough of the sequences to find the solutions.