Question

32 = 25
What is the base in this number sentence?

Answer 1

Is this using modular arithmetic?

Answer 2

\[32_k=25_m\]
Note that k>3 and m>5.

Convert to base 10:
\[3k^1+2k^0=2m^1+5m^0\\
3k+2=2m+5\\
3k-2m=3\]
Now we know that k has to be odd and m has to be a multiple of 3.
After some trial and error, we find that the smallest integers k and m satisfying the above conditions are k=5, m=6.

Answer 3

nice one, @blockcolder ...

Answer 4

Thanks. :D

Answer 5

\[32_{2 n+3 }= 25_{3 (n+1)} \]where n, an integer, is >= 1.
A solution using Mathematica Home Edition is attached.

Answer 6

Sorry. Forgot to attached the pdf solution file.