Numbers which are not the sum of distinct squares: Difference between revisions

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'''90''' == 36 + 25 + 16 + 9 + 4 == 64 + 16 + 9 + 1 == 49 + 25 + 16 == 64 + 25 + 1 == 81 + 9
'''90''' == 36 + 25 + 16 + 9 + 4 == 64 + 16 + 9 + 1 == 49 + 25 + 16 == 64 + 25 + 1 == 81 + 9
'''130''' == 64 + 36 + 16 + 9 + 4 + 1 == 49 + 36 + 25 + 16 + 4 == 100 + 16 + 9 + 4 + 1 == 81 + 36 + 9 + 4 == 64 + 49 + 16 + 1 == 100 + 25 + 4 + 1 == 81 + 49 == 121 + 9
'''130''' == 64 + 36 + 16 + 9 + 4 + 1 == 49 + 36 + 25 + 16 + 4 == 100 + 16 + 9 + 4 + 1 == 81 + 36 + 9 + 4 == 64 + 49 + 16 + 1 == 100 + 25 + 4 + 1 == 81 + 49 == 121 + 9
A
A finite number can not be generated by '''any''' combination of distinct squares:
The number of positive integers that '''cannot''' be generated by any combination of distinct squares is in fact finite:


2, 3, 6, 7, etc.
2, 3, 6, 7, etc.





;Task
;Task


Find and show here, on this page, '''every''' positive integer than can not be generated as the sum of distinct squares.
Find and show here, on this page, '''every''' positive integer than cannot be generated as the sum of distinct squares.


Do not use magic numbers or pre-determined limits. Justify your answer mathematically.
Do not use magic numbers or pre-determined limits. Justify your answer mathematically.
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