A two-digit base 7 positive integer has its digits reversed when expressed in base N.

What are the possible values of N satisfying the given conditions?

(In reply to More Bases (spoiler) by Steve Herman)

Nice job, Steve.  It, too, had used the equation 7a+b = Nb+a to find N.
N := {4,5,7,9,10,11,13,16,19,25,31,37}

11₇ = 11₇
12₇ = 21₄
21₇ = 12₁₃
22₇ = 22₇
23₇ = 32₅
31₇ = 31_{19   <-- (Thanks Charlie)}
32₇ = 23₁₀
33₇ = 33₇
41₇ = 14₂₅
42₇ = 24₁₃
43₇ = 34₉
44₇ = 44₇
51₇ = 15₃₁
52₇ = 25₁₆
53₇ = 35₁₁
55₇ = 55₇
61₇ = 16₃₇
62₇ = 26₁₉
63₇ = 36₁₃
64₇ = 46₁₀
66₇ = 66₇

Edited on October 15, 2014, 12:42 pm

Edited on October 15, 2014, 9:21 pm

Posted by Dej Mar on 2014-10-15 12:35:45