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Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

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Stage: 4 Challenge Level: Challenge Level:1
Remember that to show that a result is not true, or that a method fails, you only have to find one counterexample, that is one case where it fails. To prove that a result is always true you need a completely general argument. No matter how many cases you give where the result is true that does not prove that it is always true.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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