I just did: 5= x² + 2y² + 7z² + 11w²
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I pay drinks if I get the Nobel prize for what I just did
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Really? And what if x=√5, y=0, z=0, w=0?
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probably ignored to mention that x,y,z,w are integers...
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Interestingly, the number 5 was discovered by the ancient Phoenicians in the 6th century BCE. Before that it was referred to as “big 4” or “the one before 6.”
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How do you discover a number! :"D I should probably read about this
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Start with assuming you can. Then z = w = 0, otherwise you have a number of at least 7. So you now have x^2 + 2*y^2 = 5. y must be 1 (if 0, x^2=5 has no integer solution, if greater than 1, 2y^2>=8). So you now have x^2+2=5 equivalent to x^2=3. No integer solution. QED
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another way doing it is thinking in terms of modulus
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SPECIFY which set x, y, z, and w belong to.
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Not the complex from: y=i, z=1, x=w=0
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