document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208684>Question 1208684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of 7-digit positive integers, where the sum of the digits is divisible by 3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847086 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I have edited out the dollar signs from your question. <BR>\n" );
document.write( "It seems to be a strange copy/paste error.\r<BR>\n" );
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document.write( "The number 1,000,002 is the smallest 7-digit number where its digits add to 3.<BR>\n" );
document.write( "As such, that large number is a multiple of 3.\r<BR>\n" );
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document.write( "Then 1,000,002+3 = 1,000,005 is the next multiple of 3 and 1,000,005+3 = 1,000,008 is the next, and so on.<BR>\n" );
document.write( "This arithmetic sequence has common difference d = 3.\r<BR>\n" );
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document.write( "The nth term of this arithmetic sequence is <BR>\n" );
document.write( "a<sub>n</sub> = 1,000,002 + 3(n-1)\r<BR>\n" );
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document.write( "The largest 7-digit multiple of 3 is 9,999,999. <BR>\n" );
document.write( "We don't have to add up the digits since 9 is a multiple of 3, sums of 9 will also get us a multiple of 3.\r<BR>\n" );
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document.write( "If you solved this equation<BR>\n" );
document.write( "9,999,999 = 1,000,002 + 3(n-1)<BR>\n" );
document.write( "then you would get the result n = 3,000,000 = 3 million<BR>\n" );
document.write( "I'll let the student handle the scratch work.\r<BR>\n" );
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document.write( "Answer: 3,000,000 aka 3 million<BR>\n" );
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