perplexus.info :: Just Math : 2011 Square Sum End

2011 Square Sum End (Posted on 2012-01-14)

Determine the smallest positive integer, expressible as the sum of two nonzero perfect squares, whose base nine representation ends with 2011 (reading left to right). What are the next two smallest base nine positive integers with this property?

*** For an extra challenge, solve this puzzle without using a computer program.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The smallest positive integer that is expressible under the given conditions is:
27712₁₀ = 42011₉ = 136² + 96²
The next two smallest are given by:
With the next two smallest being:
52011₉ = 34273₁₀ = 183² + 28²
and:
62011₉ = 40834₁₀ = 197² + 45² = 195² + 53²

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

	Subject	Author	Date
	I think the answer maybe...	Dej Mar	2012-01-15 04:49:22

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