Based on my previous question which turned out to be regarding modular arithmetic, I have another question: I have two functions $$f_1=\sqrt{\left(\frac{19(8m-1)+1}{3}\right)^2+\left(\frac{22(8m-1)+1}{3}\right)^2}$$ and $$f_2=\sqrt{\left(\frac{19(8m+1)+1}{3}\right)^2+\left(\frac{22(8m+1)+1}{3}\right)^2}$$ Using modular arithmetic, $f_1^2$ and $f_2$ can be reduced to $4m_1^2+4m_2^2$ and $4(m_1+1)^2+4(m_2+1)^2$ (for some $m_1$ and $m_2$) respectively and therefore $f_1$ and $f_2$ will always be even. Is my reasoning correct? If not, can someone please point out where I am wrong?
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1Which modulus was used ? – May 28 '19 at 10:29
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modulo 3 which is the denominator of the fractions – RTn May 28 '19 at 14:44
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What's 4 mod 3 ? – May 28 '19 at 15:02
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4 mod 3 is 1. Why do you ask? – RTn May 28 '19 at 15:28
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Aka it reduces to $$(m_2+1)^2+(m_1+1)^2 \bmod 3$$ for the second and $$m_1^2+m_2^2\bmod 3$$ for the first, even/odd is mod 2. – May 28 '19 at 15:39
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Did our chat help ? – May 29 '19 at 16:46
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Indeed.. Thank you so much.. Much Appreciations! :-) – RTn May 29 '19 at 17:00