Suppose $p,p',p'',q,q',q'',q_1,q_1',q_1'',r$ are integers with $0 If $m=p\bmod r$, $m'=p'\bmod r$, $m''=p''\bmod r$ where $0\leq m,m',m'' Is there always two different integers $n,n_1$ such that
$$mq+m'q'+m''q''=\ell+n r$$
$$mq_1+m'q_1'+m''q_1''=\ell+n_1 r$$
holds where $\ell=t\bmod r$ and $0\leq \ell Can we give explicit formula for $n,n_1$?
A clarification on linear properties of modular arithmetic?
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number-theory
elementary-number-theory
modular-arithmetic
arithmetic
linear-transformations
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0Confusion arises with these strokes. What should write the equation or system to solve it. Then select those solutions which are necessary. – 2017-02-18
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0@individ I have no idea what you wrote. – 2017-02-18