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Re: progression 13^655: Find the last digit of a number...
131=13
132=169
133=2,197
134=28,561
135=371,293
136=4,826,809
137=62,748,517
138=815,730,721
139=10,604,499,373
1310=137,858,491,849
1311=1,792,160,394,037
1312=23,298,085,122,481
Notice the last digit of the number in each row is making the following pattern
3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1
The pattern 3, 9, 7, 1 repeats every four rows. Now count how many times this pattern will repeat in 655 rows. To do that, simply count how many 4-rows are there in 655.
655÷4=163 remainder 3
This simply means that there are 163 counts of full { 3, 9, 7, 1 } and the remainder represents 3 more rows. The three remaining rows in the pattern are { 3, 9, 7 }.
Thus, the last digit of 13655 is 7.