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Square sum with 5-6-7 (Posted on 2010-08-13) Difficulty: 3 of 5
Sloane’s sequences A025306, A025307 and A025308 gives the respective lists of positive integers (having at most 7 digits) that are the sum of 2 distinct nonzero squares in exactly n ways, whenever n= 5, 6 and 7.

Determine the respective maximum value and minimum value of an 8-digit base ten positive integer P, such that P is expressible as sum of 2 distinct nonzero squares in exactly n ways, whenever n = 5, 6 and 7. (P does not contain any leading zero.)

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Some bounds Comment 1 of 1

n=5: lower is <=10000625 = 5^4*16001, higher is >=99985625 = 5^4*159977

n=6: lower is <=10002425 = 5^2*53*5749. higher is >=99999925 = 5^2*877*4561

n=7: lower is <=10015625 = 5^6*641, higher is >=99953125 = 5^6*6397

 

 

Edited on August 13, 2010, 6:06 am
  Posted by broll on 2010-08-13 05:55:56

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