// Numbas version: finer_feedback_settings
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"}, "advice": "$\\var{a3} \\equiv \\var{a} \\pmod{\\var{m1}}$
\n
\n\\begin{align}
\\var{a3} &\\equiv \\var{a} \\pmod{\\var{m1}} \\\\
\\iff \\simplify[std]{{a3} - {a}} &\\equiv 0 \\pmod{\\var{m1}} \\\\
\\iff \\simplify[std]{{a3-a}} &\\equiv 0 \\pmod{\\var{m1}}
\\end{align}
\nSo the statement is {torf1}.
\n$\\var{c3} \\equiv \\var{b} \\pmod{\\var{m2}}$
\n
\nWe have
\n\\begin{align}
&& \\var{c3} &\\equiv \\var{b} \\pmod{\\var{m2}} \\\\
\\iff && \\simplify[std]{{c3} - {b}} &\\equiv 0 \\pmod{\\var{m2}} \\\\
\\iff &&\\simplify[std]{{c3-b}} &\\equiv 0 \\pmod{\\var{m2}}
\\end{align}
\nSo the statement is {torf3}.
\n$\\var{b3} \\equiv \\var{c} \\pmod{\\var{m3}}$
\n
\n\\begin{align}
&& \\var{b3} &\\equiv \\var{c} \\pmod{\\var{m3}} \\\\
\\iff && \\simplify[]{{b3}-{c}} &\\equiv 0 \\pmod{\\var{m3}} \\\\
\\iff && \\simplify[std]{{b3-c}} &\\equiv 0 \\pmod{\\var{m3}}
\\end{align}
\nWhich is {torf2}.
\n$\\var{c3}^{\\var{d3}} \\equiv \\var{g3} \\pmod{\\var{m2}}$
\n
\nWe have $\\var{c3} \\equiv \\var{k3} \\pmod{\\var{m2}}$.
\nHence $\\var{c3}^{\\var{d3}} \\equiv \\var{k3}^{\\var{d3}} \\equiv \\var{k3^d3} \\equiv \\var{g4} \\pmod{\\var{m2}}$.
\nSo this statement is {torf4}.
\n$\\var{c3}^{\\var{d4}} \\equiv \\var{h3} \\pmod{\\var{m2}}$
\n
\nWe have $\\var{c3} \\equiv \\var{k3} \\pmod{\\var{m2}}$
\nHence $\\var{c3}^{\\var{d4}} \\equiv \\var{k3}^{\\var{d4}}\\equiv \\var{k3^d4}\\equiv \\var{h4} \\pmod{\\var{m2}}$
\nHence this statement is {torf5}.
", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}