Question 1165085
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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>
So 3^123, 7^123, and 9^123 have the same last two digits as 3^3, 7^3, and 9^3.<br>
The last two digits of those numbers are 27, 43, and 29.<br>
ANSWER: 27+43+29 = 99<br>