Wednesday, November 14, 2018

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


$$12345678=949667\cdot13+\color{red}7=1122334\cdot11+\color{red}4=1763668\cdot7+\color{red}2$$ where the asked residues are in red.


No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...