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Triangular Coordinates (Posted on 2004-10-26) Difficulty: 3 of 5
Prove that there are an infinite number of distinct ordered pairs (m, n) of integers such that, for every positive integer t, the number mt + n is a triangular number if and only if t is a triangular number as well

No Solution Yet Submitted by Victor Zapana    
Rating: 2.6667 (3 votes)

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Some Thoughts Do I understand the problem? | Comment 3 of 11 |

If I assume m and n are positive I can't find any numbers that work. 

It appears I am trying to prove there are triangular numbers whose congruence class (mod m) is unique.  I don't think there are any.

 

If we allow m to be negative, then the conditions hold if n=any triangular number and m=-n.

This seems too easy.  (It may also beg the question of whether 0 or negatives can be triangular.  The statement that t is positive really makes me wonder.)

-Jer


  Posted by Jer on 2004-10-26 17:33:44
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