## BdMO National 2021 Higher Secondary Problem 11

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
Anindya Biswas
Posts: 247
Joined: Fri Oct 02, 2020 8:51 pm
Location: Magura, Bangladesh
Contact:

### BdMO National 2021 Higher Secondary Problem 11

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