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A 2547 Puzzle (Posted on 2007-03-29) Difficulty: 3 of 5
a and b are positive integers. Dividing a2 + b2 by a + b we obtain the quotient as q and the remainder as r.

Determine analytically all possible pairs (a, b) such that q2 + r = 2547

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (2 votes)

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Some Thoughts a start | Comment 1 of 4

I have made the assumption that r is the numerator of the remainder of the division result, ie. the proper fraction of the mixed number [Q  r/(a+b) ].  For if r were the remainder, in order for the equation, q2 + r, to equal a whole number, as is 2547, r would need be zero.

Two of the pairs are (24, 61) and, of course, (61, 24).

Edited on March 30, 2007, 10:15 am
  Posted by Dej Mar on 2007-03-30 00:54:54

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