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Number Theory with modulars

Source: 2024 KJMO first round

October 27, 2024
number theorymodular arithmetic

Problem Statement

Find the number of nn that follow the following:
ā˜… \bigstar The number of integers (x,y,z) (x,y,z) following this equation is not a multiple of 4. 2n=x2+2y2+2x2+2xy+2yz 2n=x^2+2y^2+2x^2+2xy+2yz
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