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# perfect powers

Best Answer superprismatic, 02 December 2013 - 02:30 AM

Spoiler for or perhaps you were thinking different squares

Go to the full post

15 replies to this topic

### #1 phil1882

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Posted 28 November 2013 - 08:27 PM

whats the smallest number that can be expressed as the sum of 3 squares in 3 unique ways

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### #2 Grimbal

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Posted 29 November 2013 - 06:29 PM

A bit cheating, but one candidate would be 125= 02 + 52 + 102  = 32 + 42 + 102 = 52 + 62 + 82

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### #3 superprismatic

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Posted 29 November 2013 - 06:44 PM

Spoiler for I get

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Posted 29 November 2013 - 06:45 PM

Spoiler for the answer is actually a lot smaller than this but

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### #5 Grimbal

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Posted 29 November 2013 - 06:47 PM

The answer depends whether you accept 0 as a square and whether you accept the same number twice.

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Posted 29 November 2013 - 06:48 PM

Spoiler for strictly zero

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### #7 superprismatic

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Posted 29 November 2013 - 07:00 PM

Spoiler for If you require the 3 squares to be different, then it's

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### #8 Perhaps check it again

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Posted 02 December 2013 - 01:55 AM

@ BMAD, your solutions do not count, because sqrt(-25), sqrt(-100), sqrt(-9), etc. are not integers.

A square (number) is the square of an integer and is necessarily nonnegative.

@ Grimbal, it is not a question of whether someone accepts 0 as a square (number).  It is a fact.

Square numbers are the squares of integers.  The phrase "in 3 unique ways" is ambiguous.

Edited by Perhaps check it again, 02 December 2013 - 02:04 AM.

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### #9 superprismatic

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Posted 02 December 2013 - 02:11 AM

Spoiler for in that case

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### #10 superprismatic

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Posted 02 December 2013 - 02:30 AM   Best Answer

Spoiler for or perhaps you were thinking different squares

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