document.write( "Question 1207720: Find the number of solutions to
\n" ); document.write( "N &\equiv 2 \pmod{5}, \\
\n" ); document.write( "N &\equiv 2 \pmod{6}, \\
\n" ); document.write( "N &\equiv 2 \pmod{7}
\n" ); document.write( "in the interval 0 \le N < 1000. \n" ); document.write( "

Algebra.Com's Answer #845746 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the number of solutions to
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document.write( "Consider the number N-2.\r\n" );
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document.write( "   N-2 = {0 mod 5},\r\n" );
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document.write( "   N-2 = {0 mod 6} \r\n" );
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document.write( "and\r\n" );
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document.write( "   N-2 = {0 mod 7}.\r\n" );
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document.write( "It means that N-2 is a multiple of 5, 6 and 7, at the same time.\r\n" );
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document.write( "The integer numbers  N-2  in the interval  [-2,998]  divisible by 5, 6 and 7  \r\n" );
document.write( "at the same time are those multiple of 210,  i.e. 0, 210, 420, 630, 840.\r\n" );
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document.write( "Hence, the solutions N under the problem's question are the numbers 2, 212, 422,  632, 842.    \r\n" );
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document.write( "In all, there are 5 solutions.    ANSWER\r\n" );
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