Determine if an integer is a palindrome in a given radix (base)

GolfScript, 10 characters

~base.-1%=

That is an easy one for GolfScript if we do it the straightforward way. The output is 0/1 for false/true.

~       # Take input and evaluate it (stack: num rdx)
base    # Fortunately the stack is in the correct order for
        # a base transformation (stack: b[])
.       # Duplicate top of stack (stack: b[] b[])
-1%     # Reverse array (stack: b[] brev[])
=       # Compare the elements

J (23 char) and K (19) double feature

The two languages are very similar, both in general and in this specific golf. Here is the J:

(-:|.)#.^:_1~/".1!:1,~1

• ,~1 - Append the number 1 to itself, making the array 1 1.
• 1!:1 - Read in two strings from keyboard (1!:1 is to read, and 1 is the file handle/number for keyboard input).
• ". - Convert each string to a number.
• #.^:_1~/ - F~/ x,y means to find y F x. Our F is #.^:_1, which performs the base expansion.
• (-:|.) - Does the argument match (-:) its reverse (|.)? 1 for yes, 0 for no.

And here is the K:

a~|a:_vs/|.:'0::'``

• 0::'`` - Read in (0::) a string for each (') line from console (` is the file handle for this).
• .:' - Convert (.:) each (') string to a number.
• _vs/| - Reverse the pair of numbers, so that the radix is in front of the number, and then insert (/) the base expansion function _vs ("vector from scalar") between them.
• a~|a: - Assign this resulting expansion to a, and then check if a matches (~) its reverse (|). Again, 1 for yes, 0 for no.

APL (20)

⎕{≡∘⌽⍨⍵⊤⍨⍺/⍨⌊1+⍺⍟⍵}⎕

Outputs 0 or 1, e.g:

      ⎕{≡∘⌽⍨⍵⊤⍨⍺/⍨⌊1+⍺⍟⍵}⎕
⎕:
      5
⎕:
      5
0
      ⎕{≡∘⌽⍨⍵⊤⍨⍺/⍨⌊1+⍺⍟⍵}⎕
⎕:
      16781313
⎕:
      64
1

Explanation:

• ⎕{...}⎕: read two numbers, pass them to the function. ⍵ is the first number and ⍺ is the second number.
• ⌊1+⍺⍟⍵: floor(1+⍺ log ⍵), number of digits necessary to represent ⍵ in base ⍺.
• ⍺/⍨: the base for each digit, so ⍺ replicated by the number we just calculated.
• ⍵⊤⍨: represent ⍵ in the given base (using numbers, so it works for all values of ⍺).
• ≡∘⌽⍨: see if the result is equal to its reverse.