MathDB

4

Part of 2010 Danube Mathematical Olympiad

Problems(1)

Prime number and equation without solution

Source:

11/3/2010
Let pp be a prime number of the form 4k+34k+3. Prove that there are no integers w,x,y,zw,x,y,z whose product is not divisible by pp, such that:
w2p+x2p+y2p=z2p. w^{2p}+x^{2p}+y^{2p}=z^{2p}.
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