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A Holiday Brain Teaser

by Brian Gladman on October 17, 2021

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)

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3 Comments Leave one →
  1. Brian Gladman permalink

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

    • Frits permalink

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

      • Brian Gladman permalink

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

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