ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 08 Oct 2013 06:14:25 -0500partitionshttp://ask.sagemath.org/question/10570/partitions/ Let f(k) be the sum of the first k odd natural numbers; that is, f(k)=1+2+ +(2k?1). Compute the values f(k) for several values. Can you see a pattern? Can you prove the pattern?
Which positive integers can be written as the sum of two squares of (nonnegative) integers? For example, 4=02+22, 5=12+22, and 8=22+22. However, 3 cannot be written as the sum of two squares. Determine which of the first 100 natural numbers can be written as the sum of two squares. What patterns do you observe? How could you gain more evidence to support your conjectures?
Tue, 08 Oct 2013 04:53:20 -0500http://ask.sagemath.org/question/10570/partitions/Comment by kcrisman for <pre><code>Let f(k) be the sum of the first k odd natural numbers; that is, f(k)=1+2+ +(2k?1). Compute the values f(k) for several values. Can you see a pattern? Can you prove the pattern?
Which positive integers can be written as the sum of two squares of (nonnegative) integers? For example, 4=02+22, 5=12+22, and 8=22+22. However, 3 cannot be written as the sum of two squares. Determine which of the first 100 natural numbers can be written as the sum of two squares. What patterns do you observe? How could you gain more evidence to support your conjectures?
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http://ask.sagemath.org/question/10570/partitions/?comment=16950#post-id-16950This is just a homework problem. Please rephrase as a specific question about Sage or it should be closed.Tue, 08 Oct 2013 06:14:25 -0500http://ask.sagemath.org/question/10570/partitions/?comment=16950#post-id-16950