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n-digit ... n-th power (Posted on 2015-10-20) Difficulty: 3 of 5
How many n-digit positive integers exist which are an n-th power?

No Solution Yet Submitted by Ady TZIDON    
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Solution answer | Comment 1 of 2
My count is 49 such positive integers exist:
11 = 1
21 = 2
31 = 3
41 = 4
51 = 5
61 = 6
71 = 7
81 = 8
91 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
64 = 1296
74 = 2401
84 = 4096
94 = 6561
75 = 16807
85 = 32768
95 = 59049
76 = 117649
86 = 262144
96 = 531441
87 = 2097152
97 = 4782969
88 = 16777216
98 = 43046721
89 = 134217728
99 = 387420489
810 = 1073741824
910 = 3486784401
911 = 31381059609
912 = 282429536481
913 = 2541865828329
914 = 22876792454961
915 = 205891132094649
916 = 1853020188851841
917 = 16677181699666569
918 = 150094635296999121
919 = 1350851717672992089
920 = 12157665459056928801
921 = 109418989131512359209

  Posted by Dej Mar on 2015-10-20 12:34:53
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