document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=430331>Question 430331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all the positive integers 'x' which when expressed in decimal notation have both of the folloing properties<BR>\n" );
document.write( "a)the firs (left-most) digit is 6<BR>\n" );
document.write( "b) when this digit is removed, the remaining integer is x/25<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298854 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=298854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose our n-digit integer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6%2A10%5E%28n-1%29+%2B+sum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29 ALIGN=MIDDLE  ALT=\"x+=+6%2A10%5E%28n-1%29+%2B+sum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29+=+%286%2A10%5E%28n-1%29+%2B+sum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29%29%2F25 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2Asum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29+=+6%2A10%5E%28n-1%29+%2B+sum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (multiply both sides by 25)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Asum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29+=+6%2A10%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"24%2Asum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29+=+6%2A10%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29+=+%2810%5E%28n-1%29%29%2F4+=+25%2A10%5E%28n-3%29 ALIGN=MIDDLE  ALT=\"sum%28a%5Bi%5D10%5Ei%2C+i+=+0%2C+n-2%29+=+%2810%5E%28n-1%29%29%2F4+=+25%2A10%5E%28n-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This simply looks for the (n-1)-digit numbers whose decimal representation is 25000...0. This means that the \"remaining\" number can be 25, 250, 2500, ... We put the 6 in front, so all integers 625, 6250, 62500, ... satisfy. </SPAN>\n" );
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