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5 Digit Number II (Posted on 2011-01-03) Difficulty: 4 of 5
In continuation of 5 Digit Number, let us define a 5-digit non leading zero base N (N > 3) positive integer x as a split number whenever, 3*x is a perfect square and, when the digits of x are split, the first number is double the second one.

How many split numbers are there whenever 11 ≤ N ≤ 36. What are the respective minimum and maximum values?

(Splitting a base-N 5-digit number into two numbers means 12345 into 1 and 2345 or, 123 and 45.)

No Solution Yet Submitted by K Sengupta    
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Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: A start. | Comment 3 of 4 |
(In reply to A start. by Jer)

Huh?  Maybe I'm not following you, Jer, but this looks like a false start to me.

x = 10000a + 1000b + 100c + 10d + e is not true for all base N > 3.

It is only true for base N = 10

Edited on January 3, 2011, 8:25 pm
  Posted by Steve Herman on 2011-01-03 17:16:55

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