perplexus.info :: Numbers : 1,3,8 ...extend!

1,3,8 ...extend! (Posted on 2017-01-26)

The set (1,3,8) has this peculiar feature:

Multiply any two of these numbers together and add 1 and you'll always get a perfect square:

1+ 1 × 3 = 4
1 + 1 × 8 = 9
1 + 3 × 8 = 25

a. Add to the above set a 4th integer, thus enabling 3 additional equalities.
b. Can you show why no 5th member maintaining the above feature exists?

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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re: results from some reading....more

| Comment 3 of 4 |

Bravo!

More: A030063 (my source)

All of us ignored ZERO as the 5th integer (forgot to disclaim it)- otherwise 0 qualifies as the 5th number.

Edited on January 27, 2017, 1:05 am

Posted by Ady TZIDON on 2017-01-27 00:58:18

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