BdMO National 2021 Higher Secondary Problem 11

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Anindya Biswas
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BdMO National 2021 Higher Secondary Problem 11

Unread post by Anindya Biswas » Sun Apr 11, 2021 10:15 pm

ধনাত্মক পূর্ণসংখ্যার কতগুলো কোয়াড্রুপল \((a, b, m, n)\) আছে যেন নিচের সবগুলো বাক্যই সত্যি হয়?
  1. \(a, b < 5000\)
  2. \(m, n <22\)
  3. \(\gcd(m, n)=1\)
  4. \((a^2+b^2)^m=(ab)^n\)
How many quadruples of positive integers $(a,b,m,n)$ are there such that all of the following statements hold?
  1. $a,b<5000$
  2. $m,n<22$
  3. $\text{gcd}(m,n)=1$
  4. $(a^2+b^2)^m=(ab)^n$
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann

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