Question 41
Given $0 \lt a \lt b \lt c$ prove that
$$
a^{20}b^{12} + b^{20}c^{12} + c^{20}a^{12} \lt b^{20}a^{12} + a^{20}c^{12} + c^{20}b^{12}.
$$
$$
a^{20}b^{12} + b^{20}c^{12} + c^{20}a^{12} \lt b^{20}a^{12} + a^{20}c^{12} + c^{20}b^{12}.
$$
MathNet 2012 Question 41
Math Olympiad Vault · MathNet 2012