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Below 5K (Posted on 2013-01-28) Difficulty: 3 of 5
N is the largest odd integer that cannot be expressed in the form
N=x 2+y2+10 z2 (x,y,z integers).

Find N .

Hint: N < 5000.

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: computer solution Comment 2 of 2 |
(In reply to computer solution by Charlie)

The program actually contained a bug, that didn't affect the answer. The second line  below should be inserted after the first line below in the original listing:

 IF n - pn > 1 AND n < 10000 AND n MOD 2 = 0 THEN max = n - 1
 IF n - pn > 2 AND n < 10000 AND n MOD 2 = 1 THEN max = n - 2

Without the second line, the result depended on the formability of the even number that follows the missing odd number. But that can't be assured; the new line catches it on the next formable odd number.

21, 87 and 133 are non-formable odd numbers that would have been missed had they been the highest, because 22, 88 and 134 are also not formable and so were not on the list of formable numbers.

Edited on January 28, 2013, 5:58 pm
  Posted by Charlie on 2013-01-28 17:55:49

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