document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=792475>Question 792475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm stuck with this problem... I don't really know how to tackle it. So if you can help me that'd be much appreciated.\r<BR>\n" );
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document.write( "Let a be a non-negative integer, written in standard decimal notation as<BR>\n" );
document.write( "akak&#8722;1 . . . a2a1a0, where 0 &#8804; ai &#8804; 9 for i = 0,1, . . . , k. Prove that a is<BR>\n" );
document.write( "divisible by 8 if, and only if, 4a2 + 2a1 +a0 is divisible by 8. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #480014 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=480014\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > digits of the number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > are, in order<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bk%5D ALIGN=MIDDLE  ALT=\"a%5Bk%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bk-1%5D ALIGN=MIDDLE  ALT=\"a%5Bk-1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, ....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B0%5D ALIGN=MIDDLE  ALT=\"a%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the non-negative integer written in standard decimal notation by the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k-3 ALIGN=MIDDLE  ALT=\"k-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > digits.<BR>\n" );
document.write( "The value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1000A%2B100a%5B2%5D%2B10a%5B1%5D%2Ba%5B0%5D ALIGN=MIDDLE  ALT=\"a=1000A%2B100a%5B2%5D%2B10a%5B1%5D%2Ba%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8%2A125%2AA%2B%2896%2B4%29a%5B2%5D%2B%288%2B2%29a%5B1%5D%2Ba%5B0%5D ALIGN=MIDDLE  ALT=\"a=8%2A125%2AA%2B%2896%2B4%29a%5B2%5D%2B%288%2B2%29a%5B1%5D%2Ba%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8%2A125%2AA%2B96a%5B2%5D%2B4a%5B2%5D%2B8a%5B1%5D%2B2a%5B1%5D%2Ba%5B0%5D ALIGN=MIDDLE  ALT=\"a=8%2A125%2AA%2B96a%5B2%5D%2B4a%5B2%5D%2B8a%5B1%5D%2B2a%5B1%5D%2Ba%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8%2A125%2AA%2B96a%5B2%5D%2B8a%5B1%5D%2B%284a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D%29 ALIGN=MIDDLE  ALT=\"a=8%2A125%2AA%2B96a%5B2%5D%2B8a%5B1%5D%2B%284a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8%2A125%2AA%2B8%2A12a%5B2%5D%2B8a%5B1%5D%2B%284a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D%29 ALIGN=MIDDLE  ALT=\"a=8%2A125%2AA%2B8%2A12a%5B2%5D%2B8a%5B1%5D%2B%284a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8%2A%28125%2AA%2B12a%5B2%5D%2Ba%5B1%5D%29%2B%284a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D%29 ALIGN=MIDDLE  ALT=\"a=8%2A%28125%2AA%2B12a%5B2%5D%2Ba%5B1%5D%29%2B%284a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%2AA%2B12a%5B2%5D%2Ba%5B1%5D=M ALIGN=MIDDLE  ALT=\"125%2AA%2B12a%5B2%5D%2Ba%5B1%5D=M\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a non-negative integer<BR>\n" );
document.write( " <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D=8n ALIGN=MIDDLE  ALT=\"4a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D=8n\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some non-negative integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8M%2B8n=8%28M%2Bn%29 ALIGN=MIDDLE  ALT=\"a=8M%2B8n=8%28M%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a multiple of 8.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D ALIGN=MIDDLE  ALT=\"4a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not divisible by 8, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D=8n%2Br ALIGN=MIDDLE  ALT=\"4a%5B2%5D%2B2a%5B1%5D%2Ba%5B0%5D=8n%2Br\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some non-negative integers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%3C=r%3C=7 ALIGN=MIDDLE  ALT=\"1%3C=r%3C=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8M%2B8n%2Br=8%28M%2Bn%29%2Br ALIGN=MIDDLE  ALT=\"a=8M%2B8n%2Br=8%28M%2Bn%29%2Br\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not a multiple of 8. </SPAN>\n" );
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