why n to the fifth ends with the same last digit
Posted September 13th, 2011 by tin_0731
example:
1^5 = 1
2^5 = 32
3^5 = 243
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For the increasing power of
For the increasing power of the digits 0,1,2,3,4,5,6,7,8,9 the respective repetition of the the same digit at the end occurs with a period of 1,1,4,4,2,1,1,4,4,2 ( for example take 3, for 3 the repetition of 3 as last digit occurs with a period of 4... 3^1=3, 3^5=243, 3^9=19683 and so on). So the common period for all the numbers will be L.C.M of 1,2 and 4, which is 4. So the fifth power of any number and the number itself will have same digit......