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Find an integer having remainders of 1, 2, 5, 5, when divided by 2, 3, 6, 12 respectively.
\n" ); document.write( "Well, intuitively, you can see that the required integer has to be equal to or larger than 12+5, right?
\n" ); document.write( "In fact, you can go farther and say that it can be equal to n*12+5, where n is any non-zero positive integer (1, 2, 3, ...).
\n" ); document.write( "Let's try some:
\n" ); document.write( "n = 1, so n*12+5 = 17
\n" ); document.write( "17/2 = 8 & R=1
\n" ); document.write( "17/3 = 5 & R=2
\n" ); document.write( "17/6 = 2 & R=5
\n" ); document.write( "17/12 = 1 & R=5
\n" ); document.write( "So 17 is such an integer and it happens to be the smallest such integer.
\n" ); document.write( "Here are some others that you can try:
\n" ); document.write( "2*12+5 = 29
\n" ); document.write( "3*12+5 = 41
\n" ); document.write( "4*12+5 = 53
\n" ); document.write( "5*12+5 = 65,... \n" ); document.write( "