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

2011 Square Sum Start (Posted on 2011-12-31)

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

How about the smallest positive integer, expressible as the sum of two positive perfect cubes, whose base ten representation begins with 2011 (reading left to right)?

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

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

Part 1
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20113 is the smallest positive integer that satisfy the given conditions since 20113 =87^2+112^2
Part 2
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2011024 is the smallest positive integer that satisfy the given conditions since:2011024=22^3+126^3
For an explanation, refer to the solution submitted by broll in this location.

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

	Subject	Author	Date
	Possible solution	broll	2012-01-04 22:45:10

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