perplexus.info :: Numbers : Multiply Sum and Sum of Squares II

Multiply Sum and Sum of Squares II (Posted on 2010-12-07)

Determine all possible values of a duodecimal (base 12) positive integer N less than 100,000 (base 12), such that N is obtained by multiplying the sum of its digits with the sum of squares of its digits.

Prove that these are the only possible values of N that exist.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The numbers in base 12 are 1, 335 and 805.
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

	Subject	Author	Date
	computer search and analytic proof (spoiler)	Charlie	2010-12-07 15:18:32

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