document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165085>Question 1165085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the last two digits of the number 3^123 + 7^123 + 9^123. </SPAN>\n" );
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document.write( "The pattern formed by the last two digits of 3 to increasing powers repeats in a cycle of length 20; the pattern for 7 to increasing powers repeats in a cycle of length 4; the pattern for 9 to increasing powers repeats in a cycle of length 10.<br><BR>\n" );
document.write( "So 3^123, 7^123, and 9^123 have the same last two digits as 3^3, 7^3, and 9^3.<br><BR>\n" );
document.write( "The last two digits of those numbers are 27, 43, and 29.<br><BR>\n" );
document.write( "ANSWER: 27+43+29 = 99<br><BR>\n" );
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