What is the smallest base-10 integer that can be represented as $12_a$ in one base and $21_b$ in another base, where $a$ and $b$ are any bases larger than 2?
1a + 2 = 2b + 1
1 = 2b - a
Let a = 5 , b = 3
125 = 213
1(5) + 2 = 2(3) + 1
7 = 7
Thank you so much!
Can you help me solve the other problem I posted about the 52 cards?