document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=974869>Question 974869</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the smallest possible integer that's greater than 100, and leaves a remainder of 1, when divided by 3; a remainder of 2, when divided by 5; and a remainder of 3, when divided by 7? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #805533 by </B><A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><B>CubeyThePenguin(3113)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><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=CubeyThePenguin><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=805533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = 1 mod 3<BR>\n" );
document.write( "x = 2 mod 5\r<BR>\n" );
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document.write( "First find the integers that satisfy the first two conditions. The first number that works is 7, the next is 22, and so on. Any number of the form 7 + 15n, where n is a positive integer, leaves a remainder of 1 when divided by 3 and a remainder of 2 when divided by 5.\r<BR>\n" );
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document.write( "7 + 15n > 100<BR>\n" );
document.write( "15n > 93<BR>\n" );
document.write( "n > 6.2 ----> n = 7\r<BR>\n" );
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document.write( "We will start looking from 7 + 15(7) = 112 and beyond. 112 is divisible by 7 and 15 leaves a remainder of 1 when divided by 7, so the number that satisfies all three conditions is:\r<BR>\n" );
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document.write( "112 + 15(3) = 157. </SPAN>\n" );
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