Monday, September 23, 2019

number theory - Find the least non negative residues mod 7,11 and 13 of 12345678.



Find the least non negative residues mod 7,11 and 13 of 12345678.



my attempt: A number N is congruent modulo 7, 11, or 13, to the alternating sum of its digits in base 1000. (For example, 123456789 ≡ 789 − 456 + 123 ≡ 456 mod 7, 11, or 13.)


Answer




What I can do if I have understood well the question is the clear



12345678=94966713+7=112233411+4=17636687+2 where the asked residues are in red.


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