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Product Crossed Pointed Ratio Puzzle (Posted on 2022-07-27) Difficulty: 3 of 5
n is a positive integer base from 2 to 36 inclusively.
Each of α and β is a nonzero digit of base n from 1 to n-1 inclusively.

Determine all possible triplets (α, β, n) such that:
(α*β)base n
-----------  is a positive integer.
(α.β)base n 
### For example, in base ten corresponding to (α, β) = (4, 5), we observe that:
(4*5)/(4.5) = 40/9, which is NOT a positive integer.

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Question re: computer solution - 3 other solutions | Comment 5 of 7 |
(In reply to computer solution by Charlie)

I compared my list of 77 with Charlie's list of 74.

These are the extra 3 solutions I had:

α β base
1 A 15
A F 21
1 K 30

or, in decimal
1 10 15
A 15 21
1 20 30

I can't figure out why the different results.

  Posted by Larry on 2022-07-28 07:41:48
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