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Post Reopened by GH from MO, Daniel Loughran, Carlo Beenakker, Mark Grant, Joel David Hamkins
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GH from MO
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Which integers can be written as Is every integer a difference of two powers?

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GH from MO
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"Latexified" the question
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Sylvain JULIEN
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True or false? (I don't know.) Every positive integer > 0 is the difference of two powers. Examples: 1 = 3^2 - 2^3$ 1 = 3^2 - 2^3 $
2 = 3^3 - 5^2$ 2 = 3^3 - 5^2 $
3 = 2^7-5^3$ 3 = 2^7-5^3 $
4 = 2^3-2^2 = 5^3-11^2$ 4 = 2^3-2^2 = 5^3-11^2 $
5 = 2^5 - 3^3$ 5 = 2^5 - 3^3 $
6 = ?$ 6 = ? $
7 = 2^5-5^2$ 7 = 2^5-5^2 $
8 =?$ 8 =? $
9 = 5^2-2^4$ 9 = 5^2-2^4 $

True or false? (I don't know.) Every integer > 0 is the difference of two powers. Examples: 1 = 3^2 - 2^3 2 = 3^3 - 5^2 3 = 2^7-5^3 4 = 2^3-2^2 = 5^3-11^2 5 = 2^5 - 3^3 6 = ? 7 = 2^5-5^2 8 =? 9 = 5^2-2^4

True or false? (I don't know.) Every positive integer is the difference of two powers. Examples: $ 1 = 3^2 - 2^3 $
$ 2 = 3^3 - 5^2 $
$ 3 = 2^7-5^3 $
$ 4 = 2^3-2^2 = 5^3-11^2 $
$ 5 = 2^5 - 3^3 $
$ 6 = ? $
$ 7 = 2^5-5^2 $
$ 8 =? $
$ 9 = 5^2-2^4 $

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GH from MO
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Post Closed as "Not suitable for this site" by Andrés E. Caicedo, abx, Chris Godsil, Wolfgang, Yemon Choi
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