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Baltic way 2009 /7

Source:

May 3, 2010
quadraticsmodular arithmeticnumber theory unsolvednumber theory

Problem Statement

Suppose that for a prime number pp and integers a,b,ca,b,c the following holds: 6\mid p+1,  p\mid a+b+c,  p\mid a^4+b^4+c^4. Prove that p∣a,b,cp\mid a,b,c.
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