Problem 44319. Write c^3 as sum of two squares a^2+b^2

Created by Mehmet OZC

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write c^3 as sum of two squares a^2+b^2. a and b must be integer and greater than zero.

For example

 5^3 = 2^2 + 11^2
 5^3 = 5^2 + 10^2
 10^3 = 10^2 + 30^2
 10^3 = 18^2 + 26^2

sort output matrix so that each row and first column is in ascending order.

Solve

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973 Solutions
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Last Solution submitted on Mar 29, 2020

Last 200 Solutions

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3 Comments

3 Comments

Stephen Cook on 16 Oct 2017

Last test case is wrong. Does not catch 500^3 == 1160^2 + 11120^2 and 500^3 == 2000^2 + 11000^2 .

James on 17 Oct 2017

First case is also wrong: 1^3 = 1^2 + 0^2. The problem doesn't specify positive numbers, so it is a valid solution. (If you *really* want to open a can of worms, a and b don't have to be integers, or even real numbers according to the test suite!)

Mehmet OZC on 18 Oct 2017

You are right James. I have add some sentences to problem definition.

Solution Comments

Solution 1289343

2 Comments

2 Comments

T. Dunker on 16 Oct 2017

Test 12: There are two solutions missing [1160 11120; 2000 11000].

Mehmet OZC on 16 Oct 2017

Thanks T. Dunker, I have corrected the mistake

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cody5 number theory

Problem 44319. Write c^3 as sum of two squares a^2+b^2

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Problem 44319. Write c^3 as sum of two squares a^2+b^2

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Last 200 Solutions

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Problem Recent Solvers253

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