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    \$\begingroup\$ Clever one) Will be there always solution to that congruence equation? \$\endgroup\$ Commented Jul 25, 2014 at 12:18
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    \$\begingroup\$ @user2992539 There will always be the trivial solutions, 1 (original image) and modulo-1 (inverted/reversed image). Most numbers have non-trivial solutions, but there are some exceptions, it seems. (related to the prime factorization of modulo) \$\endgroup\$ Commented Jul 25, 2014 at 12:26
  • \$\begingroup\$ As I understand trivial solutions lead to image similar to input one. \$\endgroup\$ Commented Jul 25, 2014 at 15:36
  • \$\begingroup\$ Correct: 1 outputs the original image, and -1 outputs e.g. imgur.com/EiE6VW2 \$\endgroup\$ Commented Jul 25, 2014 at 15:52