Question 2
a) Positive integers $a,b$ satisfy $5a\lt b$ and $a^2+ab+b^2=(b+5)^2+75$. Find the minimum possible value of $a+b$.
b) Prove that $3^{22}+5^{42}+2\cdot7^{82}$ is divisible by $11$.
b) Prove that $3^{22}+5^{42}+2\cdot7^{82}$ is divisible by $11$.